Download Lecture 2 - Earth, Atmospheric, and Planetary Physics

Lecture 1: Composition and Structures in the Atmosphere
1. Composition of the Atmosphere
i). Principle Gases
Permanent Constituents
*
Variable Constituents
Constituent
Fraction by
Volume
Constituent
Fraction by
Volume
Nitrogen (N2)
78.084%
Water Vapour (H2O)
0 - 4%
Oxygen (O2)
20.948%
Ozone (O3)
0 - 12 ppmv
Argon (Ar)
0.934%
Ammonia (NH3)*
400 ppbv
Carbon Dioxide (CO2)
340 ppmv
Nitrogen Dioxide (NO2)
Neon (Ne)
18.18 ppmv
Sulphur Dioxide (SO2)*
*
*
100 ppbv
100 ppbv
Helium (He)
5.24 ppmv
Nitric Oxide (NO)
Methane (CH4)*
1.7 ppmv
Hydrogen Sulphide (H2S)*
0.05 ppbv
Krypton (Kr)
1.14 ppmv
Nitric Acid (HNO3)
Trace
Hydrogen (H2)
500 ppbv
Nitrous Oxide (N2O)*
Trace
300 ppbv
Chlorofluorocarbons
CFCl3, CF2Cl2, CH3CCL3,
CCl4
Xenon (Xe)
89 ppbv
Hydroxyl (OH)
10 pptv (daytime)
Carbon Monoxide (CO)*
80 ppbv
Concentrations at the Earth's surface.
0.5 ppbv
ii). Particles
Aerosols - Small particles (liquid or solid suspended in air
- radius: 0.001 µm < 100 µm
Cloud Droplets
- Water condensed onto aerosol particles
- radius: 10 µm < 100 µm
Precipitation - Water drops large enough to fall to the ground
- radius: >100 µm
2. Vertical Structure of the Atmosphere
The physical processes which dominate the state of the atmosphere (thermal, chemical and
dynamical) vary with height. This is observable by the manner in which temperature and pressure
change with height.
Lecture 1, Page -2-
2.1. Vertical Temperature Structure: The Atmosphere has traditionally been separated into four
distinct regions on the basis of the temperature profile. (However, there are no impenetrable surfaces
between layers).
i). Troposphere - lowest layer of atmosphere
- only layer of atmosphere to contain life
- defined by a region of decreasing temperature with height
- average “environmental lapse rate” of -6.5(C km-1
- extends from surface to between 8 km (polar) to 16 km (tropics)
- dominated by vertical motions of air and “weather”
- top of troposphere known as tropopause (region of temperature inversion).
ii). Stratosphere
- region of increasing temperature with height
- between tropopause (12 km) and stratopause (50 km)
- increase temperatures due to strong absorption of solar radiation by ozone.
- Ozone layer
- vertically stable region
iii).
Mesosphere
iv).
Thermosphere
- region of decreasing temperature with height
- between stratopause (50 km) and mesopause (80 km)
- coolest region of atmosphere
- region of increasing temperature with height due to absorption of
short wavelength (high energy) solar radiation.
- can reach temperature in excess of 1000(C
2.2. Atmospheric Pressure: Pressure is defined as the force per unit area experienced by a surface
exposed to a gas (N m-2 or Pa). The force is exerted by collisions of gas molecules with the surface.
Consider:
a) Pressure versus Temperature
b) Pressure versus Density
Lecture 1, Page -3-
In the atmosphere, pressure at any altitude is equal to the weight of air directly above.
Sea-Surface Pressure 100 kPa = 100000 Pa = 100000 N m-2 = 10 N cm-2
= 1 kg of air above per square cm
= 20000 kg of air over a 1×2 m desk
3. Static State of the Atmosphere
The thermodynamic state of any point in the atmosphere is determined by:
Pressure
- P
Temperature - T
Density
- '
These are related by the equation of state (ie: the ideal gas law):
P = ρR * T
where R* = universal gas constant = 287 J kg-1K-1
note: M = average molecular mass of dry air = 28.96 g mole-1
3.1. Hydrostatic Equilibrium: Under static conditions (no vertical motions), the atmosphere adjusts
to a state of “Hydrostatic Equilibrium”. The downwards force due to gravity on air is balanced by
a pressure gradient force.
Consider a volume of air of thickness dz and area dA:
Lecture 1, Page -4-
Under this condition of balance, the variation of pressure in the atmosphere with height can be
d P (z )
= −ρ ( z )g
dz
expressed by the “Hydrostatic Equation”:
Thus, decrease in pressure through a thin layer of thickness dz is:
dP ( z ) = −ρ( z )g dz
To determine the pressure as a function of height in the static atmosphere, integrate the
hydrostatic equation:
- substitute for density (using the ideal gas law):
dP ( z ) = − g ρ ( z ) dz = −
- rearrange:
P (z)
g dz
R* T
d P (z )
g
= − * dz
P (z)
R T
- integrate from ground-level to a height Z:
P ( z)
dP
∫ P =
P(0)
Z
∫−
0
g
dz
R *T
- rearrange:
P ( z ) = P ( 0 ) ex p ( − z H )
Lecture 1, Page -5-
R *T
where: H =
, the scale height
g
(Note: The above derivation assumed that the temperature of the atmosphere was constant).
Appendix: Sample Questions
1) Assuming that the average daytime concentration of OH is 10 pptv, calculate the daytime
concentrations (in molecules per m3) of OH. If the average lifetime of the a OH molecule is 0.1
seconds, what is the daytime rate of production of OH (in molecules per m3 per hour)? Assuming
that each OH molecule is created by the photolysis of a water molecule, what mass of water is
destroyed (kg per m3 per hour).
2) Altitude sickness is a common problem for people when they reach altitudes over 4000 m above
sea level. Using the hydrostatic equation and assuming that the atmospheric Temperature is constant
with height at 10(C and the sea surface pressure is 101.325 kPa, calculate the pressure at this
altitude.
3) What is the total mass of the atmosphere?
4) Assuming an incompressible atmosphere with a temperature of 15(C, what height of atmosphere
would be required to produce a surface pressure of 101.325 kPa?
5) Assuming an isothermal atmosphere with a temperature of -33(C and a surface pressure of 100
kPa, esitmate the levels at which pressure equals 10, 1 and 0.1 kPa, respectively.
6) The annual Darwin Award is given to the person who did the gene-pool the biggest service by
killing himself/herself in the most extraordinary way. The 1997 Award went to Larry Water of Los
Angeles (who survived his award-winning accomplishment). He purchased 45 weather balloons and
several tanks of helium, inflated the balloons, attached them to a lawn chair and tied himself to the
chair. When he cut the cord attaching the chair to his jeep he shot up into the air and didn’t stop
climbing until about 11,000 feet. He was rescued by a helicopter but immediately arrested for
violating Los Angeles International Airports’s airspace.
Assume that the total mass of Larry, his lawn chair and the beer he took with him on his flight
was 100 kg. Assume that the surface temperature was 25(C and the “cruising” altitude temperature
and pressure was 3(C and 67 kPa, respectively. Estimate the initial and final diameters of the
balloons at Larry’s “cruising” altitude of 11,000 feet. Identify all the assumptions that were made
in coming up with your answer.
(Just in case you don’t believe me, see: http://www.officialdarwinawards.com/index.html)
Lecture 1, Page -6-
Lecture 2: Planetary Radiation Balance
1. Electromagnetic Radiation
In the atmosphere, the most important process for energy transfer is “electromagnetic (EM)
radiation”. EM radiation consists of oscillations in the Electric and Magnetic fields and can be
characterised by wavelength, frequency, amplitude, and energy . All EM wave travel at the same
speed; “the speed of light”, which is 2.998 × 108 m s-1 in a vacuum. There exists an entire spectrum
of EM waves, from long-wave radio (long wavelength, low frequency, low energy) to gamma rays
(short wavelength, high frequency, high energy). The human body can detect different regions of
the EM spectrum. The human retina is sensitive to wavelengths ranging from 0.7 µm (red) to 0.4
µm (violet). Human Skin can detect infrared radiation as heat. Within the Earth’s atmosphere, EM
radiation ranging from infrared to ultraviolet is most important.
2. Thermal Radiation (Blackbody Radiation)
• All matter emits a continuous spectrum of EM radiation in all directions, while absorbing radiation
from the surroundings.
• The properties of the emitted EM spectrum are almost independent of the material, but strongly
dependent on temperature.
• Properties of thermal radiation:
1. All objects emit radiant energy with a continuous spectrum - The Planck Spectrum
2. The hotter the object, the more energy that is emitted. Mathematically, the rate energy
emitted per unit area (flux) is (Stefan-Boltzman Equation) (in W m-2):
F = σT 4
T = Temperature (K)
) = Stefan-Boltzman constant = 5.67 × 10-8 W m-2 K-4
3. Hotter objects emit energy at shorter wavelengths than cooler objects. Mathematically, the
the wavelength of peak emission is (Wien’s Displacement Law):
where:
λ m ax =
a
T
where:
a = Wien’s Constant = 2897 µm K
4. Objects emit radiation as easily as they absorb.
3. Planetary Radiation Balance
An object in radiative equilibrium will emit radiant energy at the same rate that it is receiving
(absorbing) radiant energy from its surroundings. If the surroundings suddenly become hotter, than
the object will receive more radiant energy (F = )T4) than it is emitting. This will cause the objects
temperature to rise until it reaches a new equilibrium at which absorbed and emitted energy is
balanced. If the surroundings suddenly becomes cooler, than the opposite will occur.
If we know the amount of radiant energy being received by an object, then we can calculate an
equilibrium temperature of the object. Consider the Earth:
Lecture 2, Page -2-
i. The Solar Input
Emission of Sun in all directions (Flux × surface area of Sun) (in W):
E s = σ T s4 × 4 π R 2s
At a distance away from the Sun equal to the average distance between the Sun and Earth (Rs-e),
the total solar flux will be (in W m-2):
2
Es
4 Rs
= σ Ts 2
Fs =
R s −e
4 π R s2 −e
This quantity is known as the “Solar Constant” and has been measured to be 1360 W m-2.
The total solar energy incident on the Earth is equal to the Solar flux at the top of the Earth’s
atmosphere (Fs) times the Earth’s shadow area:
F s π R e2
However, a fraction of the radiation incident on Earth will be reflected and/or scattered back into
space by clouds, molecules and the planet surface. The fraction of radiation that is not absorbed
is called the “albedo” (A). The albedo of Earth (Ae)is approximately 0.30. (30% of incident
solar radiation is lost to space). The total solar energy absorbed by the Earth is therefore:
F s π R e2 ( 1 − A e )
In radiative equilibrium, this absorbed radiant energy will be balanced by emission of thermal
Lecture 2, Page -3-
radiation from Earth.
ii. Terrestrial Radiation
The rate that energy is emitted by the Earth is (in W):
E e = σ T e4 4 π R 2e
where Te is the “effective radiating temperature” of the Earth.
iii. Radiative Balance
Under the condition of radiative equilibrium:
Solar radiation absorbed = terrestrial radiation emitted
F s π R e2 (1 − A e ) = σ T e4 4 π R 2e
Rearranging to determine the effective radiating temperature Te:
T e4 =
F s (1 − A e )
4σ
iv. Effective Radiating Temperature
What is the effective radiating temperature of the Earth? Consider the following data:
Re = 6.378 × 106 m = 6378 km
Rs = 6.599 × 108 m
Rs-e = 1.496 × 1011 m
Ae = 0.30
Fs = 1360 W m-2
Therefore Te = 255 K = -18 (C
But the Earth’s average surface temperature is 288 K (or 15 (C). Why?
Lecture 2, Page -4-
Consider other Planets:
Planet
Albedo
Fs (of planet)
(W m-2)
Te (Calculated)
(K)
Te (Measured)
(K)
Surface T
(K)
Mercury
0.058
8876
442
442
442
Venus
0.77
2604
227
230
700
Earth
0.30
1360
255
250
288
Mars
0.15
584
216
220
210
Jupiter
0.58
50
98
130
160
4. Surface Temperature and the Greenhouse Effect
• The temperature of a planet’s surface is generally greater than its effective radiating temperature
(Te). The only case were there is no discrepancy is where there is no atmosphere (eg. Mercury).
• An atmosphere can absorb some of the thermal radiation emitted by the surface before it reaches
space. The atmosphere will then re-radiate this energy; some up to space, and some back down to
the surface. Then the effective outgoing flux from the planet will be from the atmosphere. Thus the
lower levels of the atmosphere may have much higher temperatures.
• The difference in temperatures between the surface temperature and Te depends on the opacity of
the atmosphere to IR radation.
• The following figure shows the fraction of terrestrial and solar radiation absorbed as a function of
wavelength. The atmosphere is moderately transparent in the visible region, so that much of the
solar radiation reaches the ground. However, in the IR, where terrestrial region emission peak, there
is strong absorption by minor atmospheric constituent such as H2O, CO2, and O3.
• In radiative equilibrium, the atmosphere emits energy at the same rate that it absorbs.
• The surface is heated by direct solar radiation as well as IR radiation emitted from the atmosphere.
The surface, therefore, must radiate more energy than it receives from the Sun. Therefore the surface
temperature must exceed Te.
Question: Can a planet’s surface temperature be lower than Te?
Lecture 2, Page -5-
Appendix: Sample Questions
1) Why does the amount of solar energy received at the Earth’s surface change when the altitude
of the Sun changes?
2) Given the solar constant of 1360 W m-2, what is the effective radiating temperature of the Sun?
3) As the Sun cools, its spectrum will shift towards longer wave lengths. Estimate the change in
the Earth’s effective radiating temperature Te if the peak in the peak in the Sun’s spectrum shifted
from its current peak of approximately 0.49 µm to 0.55 µm.
4) The orbit of the Earth around the Sun is elliptical, with the Earth being approximately 3.5%
closer in January than in June. Calculate the corresponding change in the Earth’s effective radiating
temperature Te.
5) Venus is closer to the Sun than the Earth, and yet has a lower effective radiating temperature.
Why?
6) Estimate the total energy from the Sun that is received by the Earth.
Lecture 2, Page -6-
Lecture 3: The Greenhouse Effect
1. A Greenhouse, and the Greenhouse Effect
The green house effect can be thought of as a 3-step process:
1. The Earth’s surface absorbs short-wavelength solar radiation
2. To keep an energy balance the Earth’s surface re-radiates IR (heat) radiation
3. Molecules in the atmosphere absorb some of the surface emission
This process is analogous to the green house, where the glass of the green house is transparent to
visible radiation but is opaque to IR. (This analogy breaks down because the glass of a greenhouse
provides a physical barrier to the motion of air and thus heat loss/transport due to convection. There
is no such barrier in the atmosphere.)
2. A Simple Model of the Greenhouse effect:
Consider a model of the Earth-atmosphere system that has the following qualities:
A flat Earth, with the incoming solar radiation distributed evenly over the entire surface.
Atmosphere transparent to incoming solar radiation, but absorbed by the Earth’s surface.
Atmosphere opaque to radiation emitted by the surface. Radiation escaping the planet must
be emitted from the atmosphere.
Atmosphere with decreasing temperature with respect to height.
A diagram of such a model is shown in the following figure:
Now consider the energy streams in the Earth-atmosphere system. S is the incoming solar energy
(in the UV-visible region) which passes through the atmosphere and is absorbed by the ground. E
is the energy emitted by the Earth’s surface (infrared). R is energy emitted from the atmosphere that
is absorbed by the Earth’s surface. And F is the energy emitted upwards from the atmosphere. It
follows that if the system is in steady state (not heating up or cooling), then the radiation emitted by
the surface must balance the energy absorbed:
E = S +R
Also, the energy emitted by the atmosphere must balance the energy absorbed by the atmosphere:
F +R = E
Also, the energy emitted at the top of the atmosphere must balance the energy entering the
atmosphere:
F =S
From this last condition, a level in the atmosphere known as the Effective Radiating Level (ERL)
can be defined such that the radiative emission is equal to the total energy emitted at the top of the
atmosphere. For the Earth, this is the altitude where the air temperature is 255 K (-18( C).
Now consider what would happen if, for some reason, the atmosphere began to trap more
infrared energy. This would cause an increase in the temperature of the atmosphere, causing the
ERL to rise and increase the energy emitted by the atmosphere to the surface (R). This in turn would
heat the surface until balance with the surface emission was achieved.
Lecture 3, Page -2-
3. The Two-Tone Model
To demonstrate the green house effect, we can consider an atmosphere which is transparent to solar
radiation and opaque to IR. In order to keep things simple, let us separate the atmosphere from the
surface of the planet, make the atmosphere a thin layer, and distribute the solar energy evenly over
the surface.
In radiative equilibrium, the upwards and downwards fluxes of radiation must balance; both at the
top of the atmosphere and at the surface.
The flux of radiation entering the atmosphere must be balanced by the amount leaving:
Q = AQ + Y
(1)
The flux of radiation on the planet surface must be balanced by the amount emitted by the
Lecture 3, Page -3-
surface:
Q + Y = AQ + X
(2)
X = 2Y
(3)
Now solve; subtract (1) from (2):
But the terrestrial radiation that is leaving the planet from the top of the atmosphere must be
(ie. The atmosphere is at the effective radiating temperature Te):
Y = σ T e4
The flux of radiation from the surface is:
X = σ T g4
where Tg is the surface temperature.
Tg =
4
2 Te =
4
2 (255 K ) = 303 K
Substituting into equation (3):
This is too warm; the average surface temperature of the Earth is 288 K, but considering the
simplicity of the model, it is not bad. How could the model be improved?
Appendix: Sample Questions
1) (a) Estimate the average energy incident at the top of the atmosphere (in W m-2)?
(b) Estimate the average energy emitted from the Earth-atmosphere system (in W m-2)?
(c) Estimate the average solar energy absorbed by the Earth-atmosphere system (in W m-2)?
2) Using the simple model of the greenhouse effect, explain how an increase in the CO2
concentration of the atmosphere would effect the ERL.
3) The simple model of the greenhouse effect did not include clouds. How might the presence of
clouds effect this model?
4) In the two-tone model described above, what is the value of Q? How is it related to the solar
constant Fs?
5) The two-tone model presented above makes a number of assumptions about the earth-atmosphere
system. A number of modifications to the model might be envisioned improve its accuracy. Some
of these include:
a) What if the atmosphere was partially transmitting in the infrared tone?
Lecture 3, Page -4-
b) What if the atmosphere was partially absorbing in the solar tone?
c) What if the atmosphere could be best modelled as two (or more) thin opaque layers (a good
approximation for Venus)?
6) a) If the solar constant for the earth were to decrease by 10%, by how many degrees would the
effective radiating temperature (Te) decrease?
b) Consider a two-tone model of the Earth. Calculate how many degrees would the surface
temperature change if the solar constant were to decrease by 10%.
Lecture 3, Page -5-
Lecture 4: Natural Variation in the Earth’s Radiation Budget
1. Globally Averaged Atmospheric Energy Balance
A model of the globally averaged energy balance of the Earth-Atmosphere system is shown below.
The input of 100 units of solar radiation on the top of the atmosphere represents the total solar input
spread over the entire surface (or Fs /4 340 W m-2). Of the 100 units of incident solar radiation,
16% is absorbed by gases in the atmosphere, 3% by clouds, and 51% by the land/ocean surface. The
rest of this incident solar radiation (30%) is back-scattered/reflected back into space; 4% by the
surface, 20% by clouds, and 6% by air molecules. In total 19% of the incident solar radiation is
absorbed by the atmosphere, 51% by the surface and 30% is reflected/back-scattered into space (the
albedo).
In order to remain in an energy balance, 51 units of energy is emitted by the surface; 7 units of
sensible heat, 23 units of latent heat, and a net IR emission of 21 units (6 units of which are not
absorbed by the atmosphere but escape to space). Note that net IR emission represent less than half
of the energy loss of the surface. Therefore, were it not for the fluxes of sensible and latent heat
(conduction and convection), the surface would be much hotter.
The atmosphere emits 133 unit of IR energy, 95 units of which are absorbed by the surface and
38 units is lost to space. The total outgoing IR from the Earth-atmosphere system is 70 units,
balancing the net solar input. Note that 64 out of 70 units (> 90%) of IR radiation lost to space
originates in the atmosphere.
Energy Budget of Surface
Incoming
Outgoing
Solar Radiation
51
Terrestrial Radiation
116
Atmospheric Radiation
95
Evaporation
23
Conduction/ Convection
7
Total
146
Total
146
Energy Budget of Atmosphere
Incoming
Outgoing
Solar Radiation
19
Radiation to Space
64
Condensation
23
Radiation to Surface
95
Earth Radiation
110
Conduction
7
Total
159
Total
159
Planetary Energy Budget
Incoming
Outgoing
Solar Radiation
100
Total
Reflected / Back-Scattered
30
Atmospheric emission to Space
64
Surface emission to Space
6
100
Total
Lecture 4, Page -2-
100
2. Variations in Solar Input
2.1 Latitude
We know from experience that the solar radiative input varies with latitude in daily and yearly
cycles. These variations are a result of changes in the orientation of the Earth’s surface relative to
the Sun. A surface which is normal to the Sun will receive more energy than one which is tilted:
Normal:
Energy Input = Fs × A
Tilted:
Energy Input = Fs × A × cos where is the “solar zenith angle” (the angle of the Sun from the vertical).
Since the Earth is spherical (almost), the Sun is directly overhead ( = 0() only at one latitude
at noon. The solar zenith angle increases away from this latitude. As the solar zenith angle
increases, the amount of energy per unit area incident on the surface decreases. Also, at higher solar
zenith angles, the solar radiation has to travel through more atmosphere. This provides more
opportunity for the solar radiation to be scattered away or absorbed before reaching the surface.
# of Atmospheres
1.00
1.02
1.06
1.15
1.31
1.56
2.00
2.92
5.70
10.80
45.00
50
40
Solar Zenith Angle
Solar Zenith Angle
0(
10(
20(
30(
40(
50(
60(
70(
80(
85(
90(
30
20
10
0
Lecture 4, Page -3-
0
20
40
60
80
100
Number of Atmospheres
In total, the incoming and outgoing radiation budget of the Earth are shown below (annual average,
June and December). They show regions of surplus and deficit energy which vary with the season.
Over the long term, these energy deviations are balanced by convective circulative motion of air.
2.2 Eccentricity
Lecture 4, Page -4-
There is a small variation in Solar input due to the eccentricity of the Earth’s orbit around the Sun.
The Earth’s orbit has a small eccentricity with the minimum and maximum distances from the Sun
being approximately147.5 × 106 km and 152.5 × 106 km. Remembering that the solar constant is
inversely proportional to the distance between the Sun and Earth (Rs-e):
R s2
Fs = σ T 2
R s −e
4
s
This eccentricity results in a variation in the Solar constant of approximately ±3% :
R

F s ′ = F s  s −e 
 R ′ s −e 
2
Eccentricity plays a only minor role in seasonal variations. In fact we are nearest the Sun around
January 3 and furthest around July 4.
2.3 Orbital Inclination (The Seasons)
The seasons are the most distinguishable feature of the Earth’s climate cycle. They are a result
of changes in the solar zenith angle and length of day, caused by the fact that the Earth’s rotational
axis is not perpendicular to the orbital plane. The angle between the orbital plane and the axis of
rotation is called the “inclination”. Since the axis of rotation does not change (always directed
towards the north star - Polaris), its orientation relative to the Sun’s rays changes throughout the
orbit.
Consider three cases.
1) Uranus has an inclination of nearly 90(:
Lecture 4, Page -5-
At one point in the orbit the north pole point toward the sun. The sun appears directly
overhead at the north pole. The entire northern hemisphere is in continuous daylight while
the entire summer hemisphere is in darkness. Half a year later, the situation is reversed.
Seasonal variations would be most extreme. In this case, a Uranus day is a Uranus year.
2) Saturn has an inclination of only 3(:
In this case, the Northern and Southern hemispheres receive about the same amount of
radiation throughout the orbit (year). Thus there are no seasonal variations. Solar input
varies only with latitude.
3) Earth has an inclination of 23.5(:
Lecture 4, Page -6-
Earth inclination results in a variation of the length of day depending on the time of year.
This results in a variation of the amount of solar energy that the northern and southern
hemispheres receive, resulting in the seasons.
(Note: Summer Solstice, Winter Solstice and the Equinoxes).
2.4 Solar Constant Variations
Lecture 4, Page -7-
The Sun is the primary source of energy responsible for governing both the weather and the
climate of Earth. For that reason alone one would expect that changes in the amount of energy Earth
received from the Sun could alter weather and climate on the Earth.
Our Sun is not a constant star and variations in the energy Earth receives from the Sun, are well
documented. The variations in solar flux are generally cyclic with times ranging from the 27-day
solar rotation period, through the 11-year and 22-year solar activity periods, to very long cycles of
hundreds to thousands of years duration.
Much meteorological and climatic data suggest that there are significant responses in Earth’s
atmosphere and oceans to variability on the part of our Sun. Drought cycles, variations in global sea
surface temperatures, variations in stratospheric temperatures at specific locations, variations in the
tracks followed by storms across the Atlantic, variations in year-to-year tree growth as determined
by tree-ring studies, and climate variations exposed by glacial ice-core studies have all shown
remarkable correlation with various forms of solar variability over time spans ranging up to 100,000
years.
• 27 Day Solar Rotation Period: This is one of the more prominent periods of solar flux variability
however the amplitude is usually much less than 0.1% and there is very little evidence of
atmospheric responses to changes of these time scales.
• 10.5 Year Solar Cycle: The most prominent period observable is that of the "Solar Cycle". It has
been observed in Chinese sunspot records dating back two thousand years. Many of the
observed changes in climate are correlated with 10.5 year solar cycle period. It has been shown
that the tracks of storms across the oceans change in latitude with changing phases of the solar
cycle. These changes in storm tracks could be the cause of droughts and floods which show
periodicities of 10.5 years in some regions of the world.
• 88 Year and 124 year and >300 year cycles: The sun has many subtle periodicities that show up
in ice core records and tree ring records that can be taken back thousands of years. These periods
are still the subject of ongoing research. The confluence of these cycles have produced climatic
changes. The most recent dramatic example of this occurred in the 17th century during which
time, the sun went several decades without sunspots. This period of solar minimum is referred
to as the Maunder minimum and the climatic changes associated with this period include severe
cold in Europe with snow in the middle of summer. In more recent times, it has been
hypothesized that between 10 and 40 percent of the increase in the Earth's temperature over the
last 100 years (global warming) could be due to an increase in the solar flux associated with the
superposition of several long-period solar oscillations.
• 23,000, 42,000 and 100,000 year cycles: Over long periods of time (thousands of years) the orbit
of the earth around the sun changes due to many factors including the gravitational pull of other
planets. The changes in the orbit will change the amount of solar radiation that the earth
receives. These variations cause major changes in the climate which cause long periods of
cooling. These periods of glaciation of much of the Northern hemisphere, referred to as Ice
Ages, have been well documented to have occurred regularly over millions of years and the
agreement between the Earth orbit around the sun and the Ice Ages is quite good.
Lecture 4, Page -8-
2.5 Volcanoes
Volcanoes have an immediate impact on the climate of the Earth and are noted to cause shortterm cooling. Emission plumes from volcanoes can extend as high as 30 into the atmosphere,
releasing massive amounts of water, sulfur dioxide and ash. Most of the heavier particles including
Lecture 4, Page -9-
ash and water rain out quickly, however, smaller particles do get ejected into the stratosphere.
Particles which reach this layer, tend remain suspended from long time periods and thus spread
around the globe. These particles (primarily H2SO4 droplets or sulfate aerosols), tend to scatter
incoming solar radiation, reducing the net solar energy flux at the surface.
Consider the effects of recent volcanoes on the global climate:
Atmospheric Transmission of solar radiation (fraction of the solar radiation that reaches the top of
the atmosphere which will pass through the atmosphere and reach the surface), measured at the
Mauna Loa Observatory, Hawaii:
Lecture 4, Page -10-
Global Average Surface Temperatures since 1860, with major volcanic eruptions marked:
Appendix: Internet
i) Volcanoes and Climate:
http://pao.gsfc.nasa.gov/gsfc/service/gallery/fact_sheets/earthsci/volcano.htm
ii) Atmospheric transmission of direct solar radiation at Mauna Loa, Hawaii
http://www.cmdl.noaa.gov/star/mloapt.html
iii) Today’s solar image:
http://www.sec.noaa.gov/today.html
iv) The Big Bear Solar Observatory
http://www.bbso.njit.edu/
Appendix: Sample Questions
1) Given the latitude of Toronto, 43.7(N, calculate the daily average solar energy reaching the
surface on equinox, summer solstice and winter solstice. How many time longer is the atmospheric
paths on these days?
2) By how much does the solar constant vary over the year due to the Earth orbital eccentricity?
Lecture 4, Page -11-
3) Describe the seasons on Uranus. Saturn.
4) Describe the seasons if the Earth’s axis were inclined 40(. Where would the tropics of Cancer
and Capricorn be located? How about the Arctic and Antarctic circles?
Lecture 4, Page -12-
Lecture 5: Global Warming and Feedback Mechanisms
1. The Greenhouse Effect
The average temperature of the Earth’s surface is substantially higher than the effective radiating
temperature (Te). This is a result of the atmosphere being radiatively transparent to solar radiation
(visible) and a strong absorber of terrestrial (IR) radiation. The main radiatively active gas is H2O
vapour. However, human activities do not directly effect the amount of H2O vapour in the
atmosphere. Instead the concentrations of other anthropogenically emitted, active greenhouse gases,
such as CO2 and methane (CH4), have been strongly effected.
2. Global Warming
There is a delicate long term balance between the outgoing terrestrial and incoming solar radiation.
Any change in the factors that affect this process of incoming and outgoing energy, or change the
energy distribution itself, will change our climate. In order to understand Global Warming, it is
important to understand both the natural and human factors effecting climate change.
2.1 Natural Factors Effecting Climate Change
Over the history of the Earth, the climate has changed. The ice ages and intervening warm periods
are examples. Some changes are global in scale, while others have been regional or hemispheric.
There are a number of natural factors which contribute to changes in the Earth's climate over various
time scales. It is important to understand these factors when attempting to detect a human influence
on climate:
Changes in Solar Output: The amount of energy radiated by the sun is not constant. There is
evidence in the temperature record of the Earth of an 11 year solar cycle (correlated to the
Sunspot cycle). Longer period changes may also occur.
Changes in the Earth's Orbit: Slow variations in the Earth's orbit around the Sun modify the
solar radiation received on Earth, affecting the amount of energy that is reflected and absorbed.
These orbital variations are believed to be a factor in initiating the ice ages.
The Natural Greenhouse Effect: The majority of the IR emission of the Earth’s surface is
absorbed by the atmosphere before reaching space. The energy is then re-emitted by clouds and
gases (such as H2O, CO2, CH4, and N2O). This helps to warm the surface, keeping it over 30(
warmer than the emission temperature of the planet, which essential for life. This is the natural
Greenhouse Effect as these gas species are naturally occurring in the atmosphere
Aerosols: These are very fine particles that are small enough to remain suspended in the
atmosphere for considerable periods of time. They both reflect and absorb incoming solar
radiation and absorb and emit in the IR. The type and quantity of aerosols in the atmosphere can
greatly affects the energy balance. (Examples: Volcanoes)
2.2 Human Factors Effecting Climate Change
With an ever increasing human population and an associated industrialisation, a number of factors
have come into play affecting the Climate of the Earth.
Enhancing the Greenhouse Effect: Naturally occurring greenhouse gases (H2O, CO2, CH4, and
N2O) keep the Earth warm enough to support life. Human activities release greenhouse gases
in large quantities. Principle in these activities is the burning of fossil fuels for the generation of
electrical energy, heating and transportation. By increasing their concentrations and by adding
new greenhouse gases like CFCs, the greenhouse effect can/has be enhanced.
CO2
CH4
NO2
CFC 12
Pre-Industrial
280 ppmv
0.8 ppm
288 ppb
0
Current
375 ppmv
1.75 ppm
315 ppb
500 ppt
Rate (per year)
0.5 %
0.9 %
0.25 %
4%
Residence Time
3 years
10 years
150 years
100 years
Land Use Change: As natural vegetation is replaced for agricultural use and asphalt, the
reflectivity and IR emissivity of the Earth’s surface is substantially altered. These changes also
affect regional evaporation, and rainfall patterns (Latent heat fluxes).
Aerosols: Humans add large quantities of aerosols to the atmosphere (both from agriculture and
Lecture 5, Page -2-
industrial activities). The effect on any global warming trends depends on the quantity and
nature of the particles. However, regional effects can be significant.
Lecture 5, Page -3-
2.3 Radiative Forcing
As greenhouse gas increases in the atmosphere, the amount of infrared energy that is emitted to space
decreases. The amount of decrease is the Radiative Forcing due to that gas. For example, radiative
transfer models have determined that if the CO2 in the atmosphere was doubled, the average
outgoing infrared radiation would be reduced by 4 W m-2 from the present value of 237 W m-2 to 233
W m-2. The projected radiative forcing of a number of greenhouse gases is shown in the following
diagram (relative to the pre-industrial atmosphere).
Lecture 5, Page -4-
2.4 Evidence of Global Warming?
The following plot are adapted from Environment Canada:
• The World’s average surface temperature since 1861:
• Global temperature variations over the past one million years (inferred)
Lecture 5, Page -5-
2.5 Climate Feedback Mechanisms
A climate feedback mechanism is a concept in which a property of the environment which is
modified by climate change will in turn affect the rate of climate change. A positive feedback
mechanism is a mechanism reinforces the climate change. A negative feedback mechanism tends
to dampen the climate change. Listed below are a few climate feedback mechanisms.
a) Water Vapour
• increased Tg increases evaporation
• increased H2O vapour increases the IR trapping of atmosphere
• enhanced greenhouse effect increases the Tg
• POSITIVE FEEDBACK
b) Ice and Snow Cover
• increased Tg increases the rate of melting
• melting decreases the surface area of ice and snow
• less snow and ice decreases the albedo (ice/snow more reflective than water/land).
• decreased albedo increases the amount of solar radiation absorbed by the surface.
• increased surface absorptions increases Tg
• POSITIVE FEEDBACK
c) Clouds
• increased Tg increases evaporation
• increased H2O vapour increases cloud cover
effect 1
effect 2
• increased clouds increase albedo
• increased clouds increase IR trapping
• cooling
• warming
• NEGATIVE FEEDBACK
• POSITIVE FEEDBACK
Lecture 5, Page -6-
Clouds play a very large role in regulating the Earth’s environment. The net effects of clouds
is a very difficult problem since the scales involved ranges from less than 10-6 m to greater
than 103 m. The radiation effects are related to the microphysics (ie. cloud particle shape,
size distribution, liquid water content, etc.) which varies substantial from cloud to cloud
(macro-scale).
2.6 Model Predictions
Modelling of the Earth’s climate response to human influences on the greenhouse effect is an
extremely difficult task. This is due to the fact that the climate system is an almost infinitely
complex system. In general, most climate models have predicted a global warming response to
human
activities
(specifically the
anthropogenic emission of
CO2). The figure to the
right show three scenarios
of global average
temperature change
(adapted from “Global
Warning... Global
Warming” by M. A.
Benarde, John Wiley,
1992). The upper scenario
being continued unchecked
emissions, and the lower
being curtailed emissions
(from 1990).
Lecture 5, Page -7-
Appendix: Internet
i) Environment Canada’s on-line references on Global Warming/Climate Change:
http://www2.ec.gc.ca/climate/primer/main_e.htm
ii) Climate Modelling & Diagnostics Laboratory
http://www.cmdl.noaa.gov/
iii) And one for those of you who think the green house effect is a big international conspiracy:
http://www.vision.net.au/~daly/
Appendix: Sample Questions
1) What is the most effective greenhouse gas in the Earth’s atmosphere?
2) What is the current radiative emission of the planet (W m-2)? What is the average radiative
emission of the planet surface?
3) Describe three climate feedback mechanisms involving water.
4) Why do we say that doubling of CO2 would cause a reduction of 4 W m-2 in the radiation emitted
to space and, at the same time we say that the atmosphere remains in radiative equilibrium?
Lecture 5, Page -8-
Lecture 6: Interaction of Radiation with Atmospheric Constituents
1. Emission and Absorption
EM radiation may also be considered as a stream of particles called photons. Photon are massless
particles which travel at the speed of light, c, and have an energy:
E = hν =
hc
λ
h = Planck’s constant = 6.6266 × 10-34 J s
= frequency (s-1 or Hz)
= Wavelength
Higher (lower) frequencies have shorter (longer) and have greater (less) energy.
where:
Molecules have different quantized energy states corresponding to different vibrational,
rotational, and electronic modes. A molecule can absorb a photon by making a transition to a state
of greater vibrational, rotational, or electronic energy. The opposite may occur for emission of a
photon. IR photon are capable of inducing changes in the vibrational and rotational states of
molecules. Shorter wavelength (higher energy) photons in the UV region are can cause electronic
transitions and, in some cases, the dissociation of molecules (break them apart).
Each atom or molecule has its
own unique set of energy states and
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2. Scattering
Scattering is a process were an interaction between a photon and a particle results in a change of
direction of the photon. In the atmosphere, scattering plays an important role in the energy budget;
specifically in the Earth’s albedo. The degree of scattering in the atmosphere depends on the size
and density of scattering particles. In general, solar radiation is scattered in the Earth atmosphere
by Rayliegh and Mie scattering
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Lecture 6, Page -2-
2.1 Rayliegh Scattering
Scattering of photons by molecules, or molecular scattering, is commonly referred to as Rayleigh
scattering (named after Lord Rayliegh, who developed the theory). A significant property of
Rayleigh scattering is that the efficiency of scattering is inversely proportional to the wavelength to
the power of four. Thus shorter wavelengths are scattered more efficiently than longer wavelengths.
Consider the ratio of the scattering efficiency of Blue light ( 650 nm) to Red ( 425 nm):
b lu e
 650 
= 

 425
re d
4
≈ 5.5
If the flux of Red and Blue light were to enter a volume of gas, over five times more Blue would be
scattered by molecules (than Red). In the Atmosphere, this produces the colour of the sky.
Blue Sky: Sunlight travelling through the atmosphere above you is scattered down towards you.
Since more Blue is scattered, the sky appears blue. Why does the sky appear much darker when
flying on a jet? Check it out.......
Red Sunset: When the Sun is on the horizon, the Sunlight travels through a much longer
atmospheric path than when directly above. Much more of the shorter Blue/Green/Yellow light
is scattered away than Red before reaching the surface.
Lecture 6, Page -3-
Lecture 7: Atmospheric Thermodynamics and Stability
1. Vertical Displacement of an Air Parcel
Let us consider a parcel of air which is moved from one height to another height within the
atmosphere. If there is no exchange of heat between the parcel and the surrounding atmosphere, then
the process is an “adiabatic process”.
The first law of thermodynamics states that the change in the total energy of a system equals the
change in the internal energy plus the work done against the surroundings. For the adiabatic
process described above, since there is no change in the total energy, then the work done on the
parcel of air equals minus the change in the internal energy.
E to t = E in t + W
= 0 for an adiabatic process
Consider the rising parcel of air:
- Surrounding pressure decreases.
- parcel expands as its pressure adjusts to the environment.
- boundaries of the parcel are doing work against the surroundings.
- as the expansion is adiabatic, the energy required for expansion comes from the internal
kinetic energy of the air in the parcel.
- the parcel’s temperature decreases in order to supply energy for the work done in
expansion. (Temperature is a measure of the speed of molecular motion.)
- the total energy of the system does not change.
The temperature of the air decreases as it rises. We will now determine quantitatively at rate
((C km-1) the temperature of a parcel of air will decrease as it moves upwards; the “Adiabatic Lapse
Rate” (
). Consider the adiabatic displacement of an air parcel from an initial state at height Z1
with temperature T1 and pressure P1 to a height Z2 with temperature T2 and pressure P2.
For the sake of keeping things simple, Lets consider a “thought experiment” in which the
displacement is carried out in three hypothetical stages; 1, 2, and 3. The three processes do not have
to be adiabatic, however the net
change in the total energy must be
zero:
∆E A + ∆E B + ∆E C = 0
By determining the energy transferred
at each stage (E) and summing to
zero, we will determine the
Adiabatic Lapse Rate (
). For
simplicity, let us consider 1 kg of air
being displaced.
Stage 1: Cool parcel to a
temperature of 0 K. (This is not
possible, but remember this is only a
thought experiment). The amount of
energy required to change the
temperature of 1 kg of air by 1(C is
the specific heat capacity (c). At
constant pressure, the specific heat capacity of air is:
c p = 1 0 0 5 J kg −1 K −1
(At constant pressure, it takes 1005 J of energy to raise the temperature of 1 kg of air by 1K).
Therefore the total amount of energy that must be removed from the parcel in the stage is:
∆E A = − c p T1
Stage 2: At T = 0 K, the parcel is lifted from Z1 to Z2. There would be no expansion in this
process since the parcel is at absolute zero. The parcel only gains gravitational potential energy:
∆E B = g (z 2 − z 1 )
Stage 3: Heat is added to the parcel to increase the temperature to T2.
∆E C = c p T 2
Now, in order for the displacement from Z1 to Z2 to be adiabatic, the change in energy over the
three stages must sum to zero.
∆ E A + ∆ E B + ∆ E C = − c p T1 + g (z 2 − z 1 ) + c p T 2 = 0
Rearranging:
T 2 − T1
g
= −
z 2 − z1
cp
or:
Γ =
dT
g
= −
≈ − 1 0 o C km −1
dz
cp
For adiabatic vertical displacement, the temperature of a parcel of air will decrease at a rate of
approximately 10(C per km (or 1(C per 100 m). The environmental lapse rate () is typically
-6.5(C km-1. This differs from what we derived above due to the release of latent heat when water
vapour condenses to form clouds. We will get to this shortly.
2. Static Stability and Vertical Air Motions:
It is a fair approximations to consider vertical air motions in the atmosphere to be adiabatic. (ie.
Vertical motions usually occur over shorter time periods than what it take to exchange energy). Then
in a dry atmosphere (no condensation), the temperature will decrease at the adiabatic lapse rate, .
Lecture 7, Page -2-
This decrease in temperature will occur independent
of the temperature of the surrounding atmosphere.
However, the rate of decrease in the temperature of
the surrounding air will determine whether the
parcel will continue to rise or descend.
d F (z + d z) = P (z + d z) d A
dA
z + dz
dA
z
2.1 Buoyancy
Consider a small cylinder of air (shown to the
right). If the air does not move in the vertical then
the gravitational and pressure gradient forces must
sum to zero:
−g ρ dz dA −
d F (z) = P (z ) d A
dP
dz dA = 0
dz
If a parcel is warmer than its surroundings it will also be less dense (ie. Lighter). The upward
pressure gradient force (which is associated with the surroundings) would be larger than the
downward gravitational force on the parcel0. This imbalance will accelerate the parcel upwards.
The opposite occurs if the parcel is cooler than the surroundings.
2.2
Stability
In order to demonstrate the conditions in which the atmosphere is stable or unstable to vertical
motions (convection), we will look at each case separately.
Case 1: Stable Atmosphere: In this case the environmental lapse rate is less than the adiabatic
lapse rate. A parcel which is displaced upwards from point “A” will cool at the adiabatic lapse rate
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(-10(C km-1). Since the temperature of the surrounding air is decreasing not as quickly, the
displaced air will be cooler. The buoyancy will force the displaced air back towards its original
position at point “A”. If the parcel is displaced downwards, it would be warmer than the
surroundings and buoyancy would push it back up.
Case 2: Unstable Atmosphere: In this case the environmental lapse rate () is greater than the
adiabatic lapse rate (
). The air displaced upwards from point “A” is warmer that its environment.
Buoyancy will accelerate the parcel further upwards. This is the condition in which convection
occurs. This is referred to as convective instability.
Convection is common near the ground on sunny days. Solar radiation warms the ground and
the air near it (by conduction). This will greatly increase the environmental lapse rate . The
heating will be greater in some areas than others and buoyancy will cause the warm air to rise. If is unstable (ie. < -10(C km-1), the air will continue to rise. If the air can rise to an altitude where
the temperature has dropped low enough for water vapour to condense, then cumulus clouds may
form. However, once condensation occurs, latent heat is released into the parcel, changing the
adiabatic lapse rate.
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3. The Thermodynamics of Water Vapour
Within the range of temperature and pressure found on Earth, water can exist in all three states: solid,
liquid and gas. Changes between these states play an important role in the Earth’s energy
budget/climate since heat is released or absorbed during the phase changes. This is referred to as
latent heat.
A familiar experience involving latent heat is the melting of ice in water. The temperature of
the water-ice mixture remains at 0(C until all the ice has melted. All the energy absorbed goes into
Lecture 7, Page -4-
the disrupting the ice crystal structure of the ice. During the freezing process, the same amount of
energy must be removed. The process of evaporation of water also requires an absorption of heat
since the molecules need extra energy to escape the liquid surface. This is why we sweat in order
to lower our body temperature. During condensation the same amount of energy is released. Two
other phase changes include deposition (water vapour to ice) and sublimation (ice to water vapour).
The energy required for sublimation equals the energy of melting plus the energy of evaporating.
A few definitions:
Vapour Pressure (e): Vapour pressure is the portion of the total atmospheric pressure which
is due to water molecules only. To a good approximation, water vapour behaves as an ideal gas:
e = ρ vR v T
where 'v is the vapour density and Rv is the specific gas constant of water vapour (461 J kg-1 K-1).
Temperature
Saturation Vapour
Pressure
-30
-25
-20
-15
-10
-5
0
5
10
15
20
25
30
35
40
45
50.88
80.7
125.4
191.18
286.27
421.48
610.78
871.92
1227.2
1704.4
2337.3
3167.1
4243
5623.6
7377.7
9585.5
Saturation Vapour Pressure (Pa)
Saturation Vapour Pressure (es): Saturation occurs when the rate that molecules are leaving
the surface is balanced by the rate of molecules returning. As the temperature increases, the rate of
evaporation or sublimation will increase. Thus the saturation vapour pressure must increase with
rising temperature.
10000
8000
6000
4000
2000
0
-30 -20 -10
0 10 20 30
Temperature (C)
40
50
Relative humidity (RH): This is the ratio of the actual amount of water vapour content to the
amount required for saturation at the temperature of the air. It indicates how near the air is to being
saturated. It can be expressed using the ratio of vapour pressure to saturation and is often expressed
in percent:
Lecture 7, Page -5-
RH =
e
× 100%
es
Supersaturation: This is a condition in which the RH is greater than 100%. This occurs when
air is cooled quickly, and the water has not condensed (Often caused by a lack of surfaces for the
water to condense to). In time, the water will condense and the air will return to saturation.
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The following diagram is a phase diagram of water. Saturated vapour pressures are given by the
line XTY’ for water and TY for ice. Water vapour is in equilibrium with either water or ice along
these lines. The line TZ is the division between ice and water. If the state does not lie on one of the
lines, then the system is not in equilibrium and will, in time exist in only one phase. Consider air
that is chilled from point “C” to point “B” (reduced temperature). This decrease will cause
condensation. However, if there is no surface for the water to condense onto, then condensation may
take some time. As a result the air will be supersaturated.
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Appendix: Sample Questions
1) Using the expression for buoyancy presented in this section, derive the hydrostatic equation.
2) Explain why in cold climates, the indoor air is always extremely dry.
3) Explain why a parcel of air that is lifted cools quicker if it is dry than if it is wet (condensed
water).
4) What is the saturation vapour pressure of room temperature room?
5) Can you think of any consequences in the environment of the saturation vapour pressure over
ice being lower than over supercooled water?
6) Can you think of what might cause unstable atmospheric conditions? Stable Conditions?
7) If a parcel of air at 25(C contained 10 g of water vapour per kg of air, what is the relative
humidity? If the temperature increased to 30(C what would the relative humidity be?
Appendix: Saturation Vapour Pressure
Lecture 7, Page -7-
Lecture 8: The Ascent of Moist air
1. The Ascent of Moist Air:
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As unsaturated air is cooled, its temperature will decrease causing the relative humidity to increase.
The amount of vapour in the air does not change, but the saturated vapour pressure decreases with
temperature. When the RH reaches 100% (or slightly greater) the vapour will begin to condense.
As the temperature drops further, more vapour will condense while the RH remains at about 100%.
The temperature to which a parcel of air must be cooled in order to have an RH of 100% is called
the “Dew Point Temperature” (Td).
Generally a cloud is formed as a result of the adiabatic cooling associated with vertical lifting
of moist air. As moist air ascends, its temperature will initially decrease at the dry adiabatic lapse
rate (
-10(C km-1). At some height, the temperature will have decreased to the point where
condensation into cloud droplets may commence. The height at which this occurs is referred to as
the “Lifting Condensation Level” (LCL). As the air continues to rise, its temperature will now
decrease at the “Wet Adiabatic Lapse Rate” (). This is smaller than the dry adiabatic lapse rate
since the latent heat released in condensation lower the rate of cooling.
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right, a parcel of air at
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stability are slightly different
than before. For saturated air (condensation occurring), the wet adiabatic lapse rate is the criterion
for stability. If the environmental lapse rate is greater than the wet adiabatic, then the air is unstable it will continue to rise. The general criterion for stability are then:
a) Absolute Stability: Absolute stability occurs when the environmental lapse rate () is less
than the wet adiabatic lapse rate. Even when stable air is forced to rise above its
condensation level it remains cooler and heavier than the surrounding air.
The most stable conditions are when the temperature is increasing with height. The is
referred to as a “temperature inversion”. This frequently occurs at night near the ground as
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it radiatively cools. The more stable the air, the more it resists vertical motions.
Temperature inversions can trap pollutants near the ground.
b) Absolute Instability: This occurs when the environmental lapse rate is greater than the dry
adiabatic lapse rate. An ascending parcel of air will always be warmer and lighter than the
surroundings; both below and above the condensation level.
c) Conditional Instability: This occurs when the environmental lapse rate is less than the dry
adiabatic lapse rate but greater then the wet adiabatic lapse rate (between about 5 and
10(C km-1). A parcel of air would experience an upward buoyant force only after rising
above its condensation level, by some means other than convection. In this case the
atmosphere is unstable only with respect to saturated air.
Absolutely Stable:
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2. Consequences of (In)Stability
2.1. Convective Clouds
Under unstable conditions (or conditionally unstable), a parcel of air may be pushed upward by
buoyancy. This typically occurs on a hot summer afternoon when solar radiation is intense and some
areas of the ground are heated more than others. This typically occurs on a hot summer afternoon
when solar radiation is intense and some areas of the ground are heated more than others (due to
variations in solar radiation absorptivities). As a parcel of air begins to rise, it will be pushed further
upwards in unstable conditions. A cumulus cloud may form if the air rises above it lifting
condensation level (LCL). If the parcel is pushed even further upwards and if there is sufficient
moisture inthe air, then this
might result in a rain shower.
Convective clouds are
associated with large updraft
velocities (1 to 30 m s-1) and
are generally as thick or
thicker in the vertical as they
are in the horizontal.
2.2. Stratus Clouds
Under stable conditions,
convective clouds do not
form. Although, there are
other processes that can move
air vertically. The clouds that
form are generally of large
h o rizontal ex tent but
vertically thin. Precipitation
from these clouds is, at most,
a light drizzle. Relatively
small and localised updrafts
of 10 cm s-1 may be
associated with such weather
systems with lateral extents
as large as 1000 km.
2.3 Temperature Inversions
(and air pollution)
When Temperature is
increasing with height, it is
Lecture 8, Page -4-
referred to as a “temperature inversion”. The air is most stable in this case and thus most resistant
to any vertical motions or mixing. The air near the ground level is cooler and heavier than aloft and
tends to stay near the ground. This has important implications for air quality since pollutants
released near the ground will be confined there by a temperature inversion.
Inversions are often formed on clear nights as the ground cools by radiating IR radiation. Since
the ground is a more effective radiator than air, it will cool faster than the atmosphere. Also, since
there are no clouds, surface emission is less likely to be trapped in the atmosphere. The air near the
ground the cools by conduction and becomes cooler than the air above.
The inversion is usually destroyed when the Sun rises and heats the surface. Inversions usually
persist within valleys since colder air sinks from the uplands to the lowlands. Unfortunately, cities
and industry is often located in lowlands. Persistent temperature inversions enhance the problem of
poor air quality.
Fog often forms when moist air cools and condenses near the surface at night and is trapped
under an inversion. If it were not for the inversions, the air would mix with drier air above and
evaporate. This is why there is often a layer of fog in low lying areas in the morning after clear cool
nights.
2.4. Changes in Stability (and thus weather)
1) Increase in Stability: Processes which cause temperature to decrease less rapidly or increase
with height. (ie. any factor that cools the surface and/or warms the air aloft).
a) Cooling of surface by radiative emission at night. May cause temperature inversions, fog,
and enhanced air pollution.
b) Warm air moving over a cold surface. Widespread fog may develop when warm moist air
from over an ocean or large lake moves over a cold surface.
c) Subsiding air heated by adiabatic compression. May induce temperature inversions.
2) Decrease in Stability (increasing instability): Processes which cause temperature to decrease
more rapidly with height.
a) Solar heating of the surface. Causes air at/near the surface to become warmer (by
conduction) than the air aloft. Convection may lead to cumulus clouds, rain, and
thunderstorms.
b) Cooler air moves over a warm surface. This heats air at ground level, but not above
(directly). When wintertime polar air moves over the Great Lakes, moisture and heat are
added to it at the surface. The air becomes unstable, generating clouds that produce heavy
snowfall on down wind shores. Buffalo receives more snow than Toronto for this reason.
c) Radiation from cloud tops. Cloud tops cool due to radiative emission while the base is
heated from IR emitted from the surface. This tends to enhance rain storms after sunset
(when cloud tops are not being heated by Sun light).
d) Lifting of air. Lifting is what is required under conditions of conditional instability. Stability
is also decreased by lifting when the lower portion of an air mass has more moisture than the
upper portion. The lower portion will saturate and its temperature will decrease at the wet
adiabatic lapse rate. This commonly occurs when moisture is trapped below the inversion
layer. For example:
Lecture 8, Page -5-
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Lift Layer A-B: Parcel at A
reaches LCL immediately then
cools at wet adiabatic lapse rate
(-5(C km-1). Parcel at B has to
be lifted at the dry adiabatic lapse
rate (-10(C km-1) until it
reaches its LCL. After that it will
cool at the wet adiabatic lapse
rate. This can result in an air
mass becoming unstable.
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adiabatically as it ascends. This cooling
may generate clouds and precipitation. Clouds and precipitation are not likely to form down
wind of the mountain since the air already lost much of its moisture and it warms adiabatically
as it descends. This is what causes “Rain Shadow Deserts” in the lee of mountains.
b) Frontal Wedging: Warm air is wedge up over cooler air.
c) Convergence at ground: Air flowing together, pushing it upwards. The height of a vertical
column of air will increase as more air flows into it.
2.4.2. Chinook winds
Those of you how have lived on the lee-side of mountains may have experienced warm, dry winds
called chinooks. Such winds are often created when a pressure system on one side of a mountain
range forces air over the mountains. As the air descends the leeward side of the mountain, it is
heated adiabatically by compression. Because condensation may have occurred during ascent,
releasing latent heat, the descending air may be much warmer (and drier) than before it ascended.
Lecture 8, Page -6-
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Appendix: Sample Questions:
1) The contents of an aerosol can are under very high pressure. When you push the nozzle on sucha
a can, the spay feels cold. Why?
2) Why does the adiabatic lapse rate of change when condensation begins? I have presented that
the wet adiabatic lapse rate is a constant ( -5(C km-1). Do you expect it to be a constant? Why?
3) Describe some weather conditions which would lead you to believe that conditions are stable or
unstable.
4) Explain why the western prairies of Canada are so dry.
5) Consider air being force over a 3500 m tall mountain range. It the air at the base of the mountain
was at 24(C and the dewpoint temperature14(C. Estimate:
a) The elevation of the cloud base?
b) Temperature at top of the mountain?
c) Amount of water vapour that condenses in moving over mountain?
d) The temperature when the air reach comes down the leeward side of the mountain?
e) The relative humidity of the air after passing over the mountain?
Lecture 8, Page -8-
Lecture 9: Formation of Clouds
1. Clouds
Clouds are composed of small spherical droplets of liquid water and/or ice crystals. These particles
are small enough that their rate of descent through the air (terminal velocity) is negligible.
The formation of a cloud droplet requires that a large number of water vapour molecules come
together. However, the saturated vapour pressure over a curved surface (such as a droplet) is greater
than over a plane surface. Molecules are less strongly attracted to a curved surface and thus
evaporate more readily. The excess vapour pressure (compared to that of a plane surface) required
for condensation to exceed evaporation (growth of a droplet) increases as the radius of the drop
decreases and its surface becomes more curved. A very large supersaturation will be required for
a small aggregate of individual molecules to be in equilibrium and grow – otherwise it will
evaporate. For example, a droplet of radius 0.01 µm requires a supersaturation of greater then 12.5%
(RH > 112.5%) to grow. This is as great a supersaturation as has ever been seen in the atmosphere.
It is too small to support the existence of droplets smaller than 0.01 µm radius. But a 0.01 µm drop
contains more than 105 molecules. These are not likely to come together by accident. In fact
supersaturation in clouds rarely exceed 1%. Thus, embryonic droplets as large as 0.01 µm will not
be able to form by homogeneous nucleation. The mechanism for creating droplets with radius less
than 0.01µm without large supersaturations is provided by aerosols. Aerosols which serve as nuclei
upon which water vapour will condense to form a cloud droplet is known as a “Cloud
Condensation Nuclei”.
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The relative humidity and supersaturation (wrt plane surfaces of
liquid water) with which water droplets are in equilibrium at 5(C.
2. Atmospheric Aerosols
Atmospheric aerosols are small particles (solid or liquid) that are always present suspended in
air. They range in size from 0.001 µm to over 100 µm radius and concentrations vary from 10-6 to
107 particles per cm3. The particles are distributed throughout the atmosphere by turbulent mixing
and direct atmospheric transport (advection).
Source of aerosols include:
a) Oceans: A major source is sea salt which is injected into air from the bursting of
bubbles, producing either small particles (film droplets) or larger particles (jet drops,
large bubbles). These aerosols are most abundant over the oceans and near coast lines
due to breaking waves. There is a rapid decrease in sea salt aerosols when moving
inland. These aerosols are very effective “cloud condensation nuclei” (CCN) since the
dissolved salt is hygroscopic.
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weathering process on deserts provide preformed particles. Dry valleys generate most
of the crystal aerosols, although soils are also a source. Sand dunes have very few
particles that are small enough for long range transport.
c) Biogenic Sources: Particles injected into the atmosphere from the biosphere include:
pollen, spores bacteria, algae, protozoa, fungi, viruses, cells of larger animals, plants, etc.
Lecture 9, Page -2-
d) Biomass Burning: Soot particles and fly ash are injected directly during burning.
Burning also releases large amounts of chemicals that can form particles in ari by gas-toparticle conversion (GPC).
e) Volcanoes: Particles can be injected directly as high as the stratosphere by volcanoes.
Volcanic ash is relatively short lived but sulphuric acid droplets remain for many years.
The most recent major eruption was Mount Pinatubo in 1991.
f) Human Activities: Human activities are a significant source, but not as much as natural
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sources. The main contributors are GPC, heavy industry, fossil fuel burning,
transportation, etc.
Sinks of atmospheric aerosols include:
a) Precipitation: Aerosols serve as nuclei for cloud droplets. When several combine to
form a rain drop, it falls towards the ground, taking the aerosols it contains and any it
collides with on the way down.
b) Impaction on Surfaces: Aerosols can be lost by colliding with a surface, such as a
window.
c) Gravitational Settling: Settling out of the atmosphere is a significant loss mechanism
for particles of radius 1µm or greater.
Properties of aerosols
a) Wettable: A wettable aerosol is an aerosol that attracts water vapour. Hygroscopic
b) Unwettable: An unwettable aerosol is one that avoids water vapour. Hydrophobic
Lecture 9, Page -3-
Adapted from: Wallace and Hobbs, “Atmospheric Science: An Introductory Survey”.
Lecture 9, Page -4-
Adapted from: Wallace and Hobbs, “Atmospheric Science: An Introductory Survey”.
Lecture 9, Page -5-
3. Heterogeneous Nucleation of Cloud Droplets
The growth of a liquid droplet depends on a couple of effects:
Curvature Effect: As described earlier, water molecules are less strongly attracted to curved
surfaces than the plane surfaces. As such, the supersaturation required for growth of droplet
increases as the radius of the droplet decreases. This relationship is proportional to the
inverse of the radius of the drop.
Solute Effect: Some of the aerosols in the atmosphere are soluble (ie. they will dissolve when
water condenses on them. This causes the equilibrium vapour pressure surrounding the
droplet to decrease (since some of the molecules on droplet surface are not water molecules).
This reduces the evaporation of the droplet without effecting the condensation. Also, the
smaller the droplet, the greater the solute effect. Thus the required saturation for growth of
droplets to grow decreases as the radius of the droplet decreases. This relationship is
proportional to the inverse of the droplet radius to the power of three.
On the understanding of these two effects, a relationship between the saturation and equilibrium
radius of a droplet has been derived, and is known as the Köhler Curve:
S = 1+
a
b
− 3
r
r
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right shows the shape of the Köhler curve for a particular drop. At small radii, the solution term
dominates. Very small droplets can exist in equilibrium at relative humidities less than 100%. As
humidity increases, the droplet will
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where the drop will continue to grow
by condensation without further
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continue to grow until the saturation
ratio drops. Such drops are called
“activated” and are CCN. In a
cloud, many droplets compete for
available vapour and tend to lower
the saturation ratio. Only a small
fraction of the atmospheric aerosols
r can act as CCN: about 1% in
continental air and about 10% to 20%
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Equilibrium saturation ratio of a solution droplet formed on an
ammonium sulfate condensation nucleus of mass 10-16 g.
Lecture 9, Page -6-
4. Nucleation of Ice Particles
Ice particles may form in air from the freezing of liquid droplets or by deposition directly from
vapour. It is possible to have unfrozen supercooled droplets at temperatures down to -40(C. Below
-40(C, any liquid drops freeze spontaneously by homogeneous nucleation (ie. no foreign ice surface
is required). Cloud composed entirely of ice are said to be glaciated.
Homogeneous nucleation of ice particles from the vapour phase requires temperature below 65(C and supersaturations greater than 1000%, (ie. it doesn’t happen, liquid drops would freeze
before such conditions were reached).
Ice crystals from by heterogeneous nucleation at temperatures above -40(C. However, ice
crystals do not form readily on most particles found in air (not as readily as liquid water). The reason
is that molecules in ice are arranged in a highly ordered crystal lattice. If a foreign substance is to
aid in the nucleation of ice, it must have a lattice structure similar to that of ice. The temperatures
at which several substances nucleate is shown in the table on the following page.
4.1 Ice Nuclei
Ice nuclei are particles in suspended in air on which ice crystals can form. For example:
Ice: Ice is the best nucleating substance as its lattice structure is exact. Any supercooled droplet
( 0(C) that comes in contact with a surface of ice will freeze.
Silver Iodide: AgI has a crystal lattice structure which is closest to ice. It is often used in cloud
seeding.
Clay Minerals: Clay minerals are natural material with a crystal structure most similar to ice.
Kaolonite is often found in snow crystals.
Organic materials: Even though not being chemically similar, are efficient ice nuclei.
Lecture 9, Page -7-
Crystal Lattice Dimension
Substance
a axis (')
c axis (')
Temperature to
Nucleate ((C)
4.52
4.58
4.54
3.8
4.65
4.36
4.2
4.24
4.78
7.36
7.49
6.86
16.43
5.11
12.34
9.5
6.84
9.77
0
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-6
-7
-7
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-8
-12
-12
4.12
5.16
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5.34
4.14
8.56
7.38
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-13
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Comments
Insoluble
Slightly Soluble
Insoluble
Insoluble
Insoluble
Insoluble
Soluble
Soluble
Pure Substances
Ice
AgI
PbI2
CuS
CuO
HgI2
Ag2S
CdI2
I2
Minerals
Vaterite
Kaolinite
Volcanic Ash
Halloysite
Vermiculite
Cionnabar
Silicate
Organic Materials
Testosterone
Chloresterol
Metaldehyde
-Napthol
Phloroglucinol
Bacterium
Pseudomonas Syringae
Lecture 9, Page -8-
Bacteria in Leaf
mold
4.2 Modes of Crystal Formation
There are four modes of ice crystal formation shown schematically in the following figure. They are:
a) Heterogeneous Nucleation/Deposition: Ice formed directly on the nucleus from the vapour
phase.
b) Condensation Nucleation: Ice formed by the homogeneous freezing of a liquid particle.
c) Contact Nucleation: Droplet freezes when an ice nucleus in air comes in contact.
d) Immersion Freezing: Nucleation caused by another nucleus (other then the CCN) suspended
in supercooled water droplet.
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1) Can a cloud droplet exist in a stable condition if the relative humidity is below 100%? If so,
how?
2) Can you think of any examples of homogenous nucleation of water droplets in your everyday
experience?
3) Why is a good droplet nucleation aerosol not necessarily a good ice nuclei?
4) By what physical mechanisms does a solute reduce the evaporation from a droplet?
Lecture 9, Page -9-
Lecture 10: Precipitation and Charge Generation
1. The Initiation of Warm Rain
Much of the World’s precipitation occurs
Larg e C loud D rop
r = radius in µ m
in the tropics from clouds at temperature
n = num b er per litre
r = 50, n = 1 0 , v = 27
greater than 0(C. The process initiating
v = te rm inal velocity in m s
this warm rain then involves only liquid
water.
Typical C loud D rop
The figure to the right show the spread
r
=
10, n = 1 0 , v = 0.1
C onventional
in the sizes of cloud droplets. There is a
bord er-line
continuous spectrum of droplet sizes
betw een clo ud
drop s and
found within any cloud.
raindrops
Typical C ondensation N uclei
Larger heavier droplets fall at greater
r = 100
r = 0.1, n = 10 , v = 0.0001
v=7
speeds than the smaller lighter ones. A
rain drop is a large cloud droplet that is
large enough to fall to the ground before
Typical R aindrop
evaporating into the unsaturated air below
r = 1000, n = 1, v = 65
the cloud. The smaller cloud droplets fall
more slowly and would evaporate before
falling very far below the cloud base.
In forming raindrops, cloud droplets must increase in volume by more than a factor of 1000. It
is known that rain can develop within 20 minutes of cloud formation. Condensation can not explain
this rapid growth.
Collisions and Coalescence of cloud droplets can explain the rapid development of warm rain.
Large droplets fall through the smaller droplets. As the smaller droplets collide with the larger ones,
there will be coalescence much of the time. There is a continual tendency for large drops to grow
and smaller drops to disappear. For example:
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The large drops are potentially capable of sweeping up the smaller drops located between the broken
lines above. The larger drops grow at the expense of the smaller ones. If there is an updraft (as in
a cloud), the large drops will take longer to fall through the cloud and the growth process is
extended. This is demonstrated in the following “quantitative model” of the production of a large
rain drop within a warm cumulus cloud.
The drop leaves the
base of the cloud with a
µ
radius of 2.5 mm. This
process is enhanced when
the drop grows larger and
breaks apart as their
s u rface tension is
overcome by the
frictional forces of the
passing air and/or
collisions. The fragments
then rise again in the
updraft and grow again to
repeat this process; a
µ
µ
chain reaction. This lead
to heavy rainfall. The
steps in the process are as
follows:
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1.1. Collision and Coalescence
Since the terminal velocity of a drop increases with the size of drop,
cloud droplets that are slightly larger than the average will have a
slightly higher fall velocity than the average. These larger drop might
collide with smaller drops lying in its fall path and coalescence may
occur. Consider a drop of radius r1 (we shall call the collector drop)
which is overtaking a smaller droplet of radius r2. As the collector drop
approaches the droplet, it will tend to follow the air streamlines around
the collector drop and might miss collision (and coalescence). We can
define an effective collision cross-section r* (shown in the figure to the
right) which represents the critical distance between the centre line of
the collector drop (fall direction of the centre of the collector drop) and
the centre of the droplet such that all droplets within the distance will
collide with the collector drop. Conversely, any droplet outside this
distance will not collide. Therefore, the effective cross-section of the
collector drop is then %r*2, whereas the geometrical collision crosssection is %(r1 + r2)2. We can therefore define the “Collision
Efficiency” (e) as:
Lecture 10, Page -2-
r
1
r
r*
2
e =
(r
1
r *2
+ r2 )
2
Determining the value of collision efficiency is an extremely difficult mathematical problem. The
results of one computerised model is shown below; showing the collision efficiency as a function
of the ratio of r2 / r1. This model shows that when the collector drop is much larger than the droplet
(r2 / r1 « 1), collision efficiencies are small because the droplet tend to follow closely to the
streamlines around the collector drop. A the ratio increase, the efficiency increases rapidly (droplets
less likely to follow streamlines). Also note that efficiencies can be greater than unity (1) when the
drops are nearly the same size due to wake effects behind the collector drop. It should also be noted
that collisions do not necessarily mean coalescence (see diagram below).
As a drop falls through a cloud, it may become so large and unstable that air currents and/or
droplet collisions might break it apart. When this occurs, it produce two or more large drops,
starting a chain reaction that allows the formation of a large quantity of raindrops.
Calculated values of collision efficiency for collector
drops of radius of radius r1 with droplets of radius
r2 .
(a) A stream of water droplets of about 100 µm
rebounding from a layer of water. (b) At an
increased angle, droplets coalesce.
Lecture 10, Page -3-
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Lecture 10, Page -4-
2. The Initiation of Cold Rain
If a cloud extends above the 0(C level, it is called a cold cloud. Cold clouds may contain
supercooled water droplets and/or ice particles. If a cloud contains both, it is said to be a “mixed
cloud”. If it is entirely ice particles, the cloud is said to be “glaciated”.
2.1. Ice crystal Shapes
The shape that an ice crystal forms while growing by deposition is sensitive to the ambient
temperature and supersaturation. The basic crystal habit is a hexagonal face (six sides). If the axis
normal to the hexagonal face is long, it is called “prism-like”; if short
then “plate-like”.
The surface to volume ratio if greatest for fernlike dendrites.
Dendrites form when the temperature is about -15(C, when the growth
rate is greatest. This crystal structure provide ambient vapour more
surface on which to deposit.
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Plate-like
Hexagonal Plates
-4 to -10
Prism-like
Columns
-10 to -12
Plate-like
Sector Plates
-12 to -16
Plate-like
Dendrites
-16 to -22
Plate-like
Sector Plates
-22 to -50
Prism-like
Columns
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2.2. Growth of Ice Crystals
a) Growth by deposition: In a cloud that contains a large fraction of
supercooled droplets, the air in the cloud will be saturated with
respect to liquid water. However, under these conditions, the
air will be supersaturated with respect to ice. (At -10(C, air that
is saturated with respect to liquid water will have a
supersaturation of 10% with respect to ice). As a consequence,
the ice particles in a mixed cloud will grow at the expense of
the water particles.
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Lecture 10, Page -5-
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The phase diagram of water. Saturated vapour pressures are given by the line XTY’ for water and TY
for ice. Water vapour is in equilibrium with either water or ice along these lines. The line TZ is the
division between ice and water.
b) Growth by riming; hailstones: Riming is the process by which supercooled drops freeze when
coming in contact with an ice particle. In the extreme, this process can result in the
formation of graupel and hail.
c) Growth by Aggregation: Aggregation is the process by which ice particles collide and clump
together to form larger particles. The adhesion of colliding ice particles depend on the
temperature. In general, the higher the temperature, the stickier the surfaces. Also, dendrites
tend to become entwined.
3. Charge Generation (Separation)
All clouds are electrified to some degree. However, in some convective clouds, the electrical
charges that build up are strong enough to give rise to thunderstorms. The average thunderstorm
Lecture 10, Page -6-
(shown in the figure
to the right) contains
a net positive charge
( +24 coulombs) in
the upper (glaciated)
regions, a net negative
charge ( -20
coulombs) in the
lower (mixed) region
just above the
freezing line, and a
small net charge (
+4 coulombs) below
the melting level. There are three theories as to the cause of charge separations in clouds. The first
two deal with a phenomenon known as the “thermoelectric effect” in ice. In a rod of ice, if there
is a temperature difference from one end to the other, there will be a small charge separation within
the rod; with the colder end having a slight negative charge. The theories of ice particle development
are:
a) Ice particle collides with a hailstone whose surface is warmed by riming. Ice particle rebounds
with positive charge and hailstone receives negative. The hailstones continues to fall while the
ice crystal is taken upwards in by updraft.
b) Supercooled droplet collides with hail stone. During freezing of droplet, a negatively charged
ice splinter is ejected.
c) A precipitation and a cloud particle, both polarised by a down-ward directed electric field,
collide. Negative charge transferred to precipitation particle during contact and cloud particle
rebounds with positive charge.
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Lecture 10, Page -7-
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Appendix: Sample Questions
1) Can Collision Efficiency be larger that 1? What does this mean?
2) Are collision and coalescence synonymous?
3) How does hail form? What factors govern the ultimate size of hailstones?
4) What is the volume of a typical cloud droplet? What is the volume of a large raindrop? How
many cloud droplets have to collide to form a raindrop?
5) What is the swept-out area of a 5 mm diameter drop? A 1 mm diameter drop?
Lecture 10, Page -8-
Lecture 11: Cloud Morphology and Severe Storms
1. Lightning
Cloud-to-ground lightning originates near the cloud base in a discharge called a stepped leader,
which moves downward towards the Earth in discrete steps. Each step lasts about 1 µs in which the
leader advances about 50 m, with a time of approximately 50 µs between steps. It is believed that
the stepped leader start by a local discharge in the bottom of the cloud. As the negatively charged
stepped leader approaches the ground, it induce positive charges on the ground (especially protruding
objects). When the stepped leader is close to the ground(10 - 100 m), a stroke moves up from the
ground to meet it. A connection is made and a large current produces the lightning stroke. After the
first stroke of electricity, a number of subsequent strokes can occur; usually within 100 ms of the
previous stroke. Most lightning flashes contain 3 or 4 strokes. A lightning stroke can raise the
temperature of the air inside the channel of the it passes through to above 30,000(C and pressure of
100 atmosphere, before the air has time to expand. The channel expands rapidly creating a powerful
shock wave which we hear as thunder.
2. Cloud Morphology
2.1. Mechanisms for Formation
Clouds form in air which has become supersatured, usually through ascent accompanied by adiabatic
expansion and cooling. The principle types of ascent, each of which produces distinct cloud forms,
are:
• Local Ascent of warm buoyant airparcels in a unstable or conditionally unstable environments,
which produces convective clouds. These clouds, in the form of cumulus or cumulonimbus,
have diameters range from 100 m to 10 km with updrafts velocities in the range of a few m
s-1. Lifetimes of these clouds range from minutes to hours.
• Forced lifting of stable air which produced layer clouds. These clouds, in the form of stratus,
can form from ground level up to the tropopause and extend over to thousands of kms.
Lifting rates rang in the few cm s-1, and lifetimes are over periods of tens of hours.
• Forced lifting of air over hills or mountains produces orographic clouds. Updraft velocities
depend on height of topography, speed of winds, but can be several m s-1.
Other processes other than lifting which lead to the formation of clouds include
• Cooling of air when it comes in contact with a cold surface. Most common form is fog:
radiation fog when ground cools by radiative emission on windless nights and advection fog
when warm moist air moves over a cold surface.
• Adiabatic expansion and cooling due to a rapid local reduction in pressure; responsible for
formation of funnel clouds associated with tornadoes.
2.2. Types of Clouds
The international cloud classification system was proposed by Luke Howard in 1803 and based
on Latin names.
Cumulus: A pile or heap. Convective clouds
Stratus: A layer. Layer clouds
Cirrus: A filament of hair. Fibrous clouds.
Nimbus:
Rain clouds. Used only in composite names; (such as nimbostratus or
cumulonimbus).
Alto: Middle. Indicates middle level clouds. Used only in composite names; (such as
altostratus or altocumulus).
Lecture 11, Page -2-
2.2.1. Convective clouds
• Cumulus, Cumulonimbus
Lecture 11, Page -3-
2.2.2. Layer Clouds
• Cirrus, Altostratus, Nimbostratus, Altocumulus, Stratocumulus, Cirrocumulus
Lecture 11, Page -4-
2.2.3. Orographic Cloud
Orographic lifting can result in varoius different cloud types over various heights. Their formation
is due to lifting of air over a surface feature such as a mountain. The motion of the air results in
known as a mountain wave, and can be produced. On the lee-side of the mountain, the clouds will
evaporate in down-ward moving air, resulting in regions of low seasonal rainfall known as rain
shadows. Sometimes, on the lee-side the mountain will induce and vertical oscillation known as lee
waves, which can result in lee-wave clouds.
3. Air-Mass Thunderstorm
Air-mass thunderstorms occur widely in the tropics and mid-latitudes, when humid air drift over
continental regions during the summer. The following is an idealised three stage model of the life
cycle of an air-mass thunderstorm. In the first stage, known as the “Cumulus stage”, the cloud
consists entirely of a warm buoyant plume of uprising air, with air being entrained into the cloud
from the sides and bottom. Air at the top of the cloud has updrafts on the order of 10 m s -1. Because
of this large updraft, supercooled liquid cloud droplets exist above the freezing line, which is pulled
upwards with the updraft. The second stage, known as the “Mature stage”, is characterised by the
formation of a strong downdraft coinciding with the region of greatest rainfall. The downdraft is
formed by frictional drag on the air from the falling raindrops and is cooled by evaporative cooling
of raindrops below the cloud base. Supercooled droplets exists above the freezing line in the updraft
region, and below the freezing line in the downdraft. Maximum updrafts are in the middle of the
cloud, and maximum updrafts are found near the bottom of the cloud. As precipitation develops
Lecture 11, Page -5-
throughout the cloud, the downward motion takes over the cloud. This is the third stage, known as
the “Dissipation stage”. Deprived of the
updraft of supersatured air, cloud
droplets no longer grow and
precipitation soon ceases.
In general, only about 20% of the
water vapour that condenses in a cloud
reaches the ground in precipitation. The
remainder either evaporates or breaks up
into smaller clouds (such as cirrus). Airmass thunder storms are generally short
lived and sometime produce destructive
winds and hail.
3.1. Hail
Hailstones is precipitation in the form of
hard pellets or lumps of ice. Generally
hail stones have diameters of between 1
and 5 cm. Under extreme conditions,
Lecture 11, Page -6-
they can be larger. The largest recorded hailstone fell in Kansas in 1970 and was 14 cm in diameter
and weighed 766 g. It estimated speed when it hit the ground was in excess of 160 km h-1.
Hailstones represent an extreme case of the growth of an ice particle by riming. They form in
clouds which have high liquid water content. Hail begins as a small ice pellet or “graupel” that
grows by riming of supercooled water droplets. Its surface temperature may rise to 0(C due to the
release of the latent heat of freezing, and some of the collected water may remain unfrozen. If the
pellet encounters an updraft, it can be carried aloft only to begin another downward journey. This
may happen a number of times before the hailstone leaves the cloud.
If a hailstone is cut into thins sections and view in transmitted light, it often consists of dark and
light layers. These layer result from changing conditions in the hailstone formation as it moves
through the cloud. The dark layers result from trapped air bubbles which correspond to rapid
freezing of coalesced water droplets. The clear section is where there is no trapped air and
correspond to when the hailstone was growing wet.
Lecture 11, Page -7-
3.2. Multi-Cellular Thunderstorms
A multi-cellular thunderstorms is a large thunderstorm system comprised of a number of individual
storm-cells at different stages of development. These tend to be the most severe form of
thunderstorm and form under conditions of veering winds with height. In cases of severe multicellular storms it is observed that the individual storm cell will move along the mid-tropospheric
wind direction while low-level windows come in from the right. Because the low-level inflow
comes in from the right, the storm-cells originate in the right and dissipate to the left. Continuous
generation of new cells on the right propagates the multi-cellular thunderstorm.
Lecture 11, Page -8-
Lecture 12: Atmospheric Dynamics I
1. Fundamental Forces
The motions of the fluids (such as air) is governed by the fundamental laws of physics.
However, the Earth’s atmosphere moves in a rotating (or accelerated) coordinate frame. Newton’s
Law’s of motion can only be applied if the acceleration (rotational acceleration) of coordinate frame
is taken into account. This is done by introducing a number of a number of apparent forces.
1.1. Real Forces
Real forces that act on a parcel of air
include pressure gradient forces, gravity
and friction (exerted by neighbouring
parcels of air of a surface).
z
ds
1.1.1. Pressure Gradient Force
Consider the horizontal pressure gradient
P + dP
dz
force on a parcel of air with a height dz P
and a width of dn (where n is a
horizontal direction with a pressure
gradient, and s is the horizontal direction
perpendicular to n). By the same logic
n
dn
used in Lecture 1 to derive the
hydrostatic equation, we can derive the a
horizontal pressure gradient force. Assuming that the pressure gradient over the distance dn is
small, then we can approximate that the horizontal change in pressure is:
dp ≅
dp
dn
dn
But pressure is defined as the force per unit area, therefore, the horizontal force on the parcel is:
Fn = −
dp
dn ds dz
dn
where the negative sign indicates that the force is directed in the opposite direction to the direction
of increasing pressure. If we divide by the mass of the air in the parcel (' dn ds dz), where ' is the
density of the air, we obtain the pressure gradient force per unit mass:
1 dp
Fn
=−
ρ dn
m
Similarly, the vertical pressure gradient force is:
Fz
1 dp
=g=−
m
ρ dz
It is important to note that the force is proportional to the gradient of the pressure field, not to the
pressure field itself.
1.1.2. Gravity
m
newton’s law of gravitation states that the force of gravity
between on an object of mass m due to an object of mass M,
separated by a distance r is equal to:
Fg = −
M
r
GMm
r2
where G is the universal gravitation constant (G = 6.673 × 10-11 N m2 kg-2 ). The force per unit
mass (the gravitational acceleration) on the atmosphere by the gravitational attraction of the Earth
is:
Fg
m
*
= g* = −
GM
r2
-2
where g = 9.81 m s at sea level.
1.1.3. Friction
Throughout most of the atmosphere, frictional forces are sufficiently small and can, to first order
be neglected. A notable exception is the planetary boundary layer corresponding to roughly the
lowest 1 km of the atmosphere where frictional drag forces due to the surface and turbulence can be
large.
1.2. Apparent Forces Acting in a Rotating
Coordinate System
Consider an object being rotated about a
central point. In order for the object to
remain in circular motion there must be an
inwards directed force called the centrifugal
force. For example consider a ball on a
string. In order to maintain circular motion,
the string pulls the ball inwards. The
acceleration of the ball towards the centre is
Lecture 12, Page -2-
known as the centripetal acceleration (ac):
v2
ac =
r
The Earth rotates with a period of one day. Therefore it has an angular velocity 7 of:
ω = 2 π ra d d ay −1 = 7 .2 9 2 × 1 0 −5 s −1
Now consider an object that is travelling on the Earth’s surface with a zonal (east-west) velocity of
u (a north-south velocity is called a meridional velocity). The zonal velocity u is defined as
positive if the relative motion is in the same sense as the Earth’s rotation (u > 0, westerly flow); and
negative if opposite (u > 0, easterly flow). Therefore, to an observer outside the Earth’s rotation
frame, an object travelling on the surface of the Earth with a zonal velocity of u will have a total
velocity of (7R + u). Because the parcel is travelling in circular motion, it has an acceleration
towards the centre of the Earth of:
ac
(u + ω R ) 2
v2
u2
2
=
=
= ω R + 2ωu +
R
R
R
From the viewpoint of someone standing on the Earth, the centripetal acceleration is only u2/R (the
real force) and yet there are two more terms. This apparent violation of Newton’s laws can be
eliminated by introducing apparent forces per unit mass of 72R (a static term) and 27u (a linear
term), directed away from the axis of rotation.
1.2.1 Gravity
A mass on the surface of the planet will experience
a gravitation force mg* directed towards the centre of
the planet. However, due to the rotational motion of
the planet, a component of the gravitational force is
used to supply the centrifugal force. Therefore, in
vector form:
7" r
R
J
J
&
& &*
2
g=g +ω R
The gravitational force is directed towards the centre
of the Earth whereas the centrifugal force is directed
away from the axis of rotation. Therefore, except at
the poles and the equator, gravity is not directed
towards the centre of the planet. The Earth, however, has adjusted to this effect as the equatorial
radius is 21 km larger than polar radius. As a result, the local vertical does not pass through the
centre of the planet; except at the poles and the equator.
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Lecture 12, Page -3-
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DXUbUV_bUdXUSXQ^WUY^dXUV_bSU_VWbQfYdi_^dXU`Ubc_^Yc*
∆F = Fp o le − F e q = m ω 2 R e
∆F = ( 8 0 kg )( 7 .2 9 2 × 1 0 −5 s −1 ) 2 ( 6 .3 7 × 1 0 6 m ) = 2 .7 1 N
1ddXUUaeQd_bdXUV_bSU_VWbQfYdiQ``UQbcd_`e\\_^dXU`Ubc_^gYdX"'>\UccV_bSU
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∆m =
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∆F
= 0 .2 8 kg
* =
9 .8 1 m s −1
g
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1.2.2. The Coriolis Force
The second apparent force is the Coriolis force and
is fundamentally different from the 72R term in that
Lecture 12, Page -4-
it is dependent of the zonal velocity
u. It is directed outwards from the
axis of rotation in a westerly motion,
and inward in an easterly motion.
For westerly motion, the horizontal
component of the Coriolis force
pushes the object equator-ward. The
Coriolis force also arises for motions
moving radially towards or away
from the axis of rotation. This is due
to the principle of conservation of
angular momentum. In a meridional
motion, the conservation of momentum induces a zonal motion
due to the Coriolis force. In the northern hemisphere, the Coriolis Force results in motions being
deflected to the right (and deflected to the left in the Southern hemisphere). Consider a region of low
pressure in the Earth’s atmosphere. If the Earth was not rotating, the winds would blow inwards
towards the low. But in a rotating atmosphere, the winds are deflected to the right setting up a
counter-clockwise flow (clockwise in the Northern-hemisphere).
Lecture 12, Page -5-
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Appendix: Sample Questions:
1) Consider a person who’s mass is 80 kg (176 lbs). How much less is the force of gravity on this
person at 45( latitude than at the poles? What is the apparent change in mass of the person?
2) How long would an average day be if the Earth rotated so fast that the centifugal force equalled
the force of gravity at the equator?
Lecture 12, Page -6-
3) It is a common belief that in the Northern hemisphere when you pull a plug in a drain, the water
will flow to create a counter-clockwise vortex over the drain. (And clockwise in the Southern
hemisphere). This effect is attributed to the Coriolis force. Can you estimate how large this force
is on the vortex? Does this explanation seem plausible?
4) Consider a person who’s mass is 80 kg (176 lbs) and is riding in a car on the equator. By how
much is the apparent force of gravity on this person changed when the car is travelling eastward
compared to westward? Compare this to the same person standing on the pole.
Lecture 12, Page -7-
Lecture 13: Atmospheric Dynamics II
1. Geostrophic Winds
Under conditions where there are no frictional forces or other forces arising from thermal effects
and curvature of flow, the motions of air are a product of the Coriolis force and the pressure gradient
forces. A flow of air under a condition of balance between these forces, is known as a geostrophic
wind. Such winds, which form in the layer of the atmosphere above the boundary layer (above
approximately 1 km), the tends to be smooth and locally uniform.
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Consider a parcel of air that is initially at rest in a pressure field as shown in the figure to the
right. The parcel will begin to move towards the lower pressure. As the velocity of the parcel
increases, the Coriolis force which pulls the parcel to the right (in the northern hemisphere)
increases. This deflects the parcel to the right until a balance is reached between the pressure
gradient wind and the Coriolis force. At this point the winds will blow the parcel parallel with the
isobars as the geostrophic winds.
The geostrophic balance is only valid for situations where the Coriolis force is large. Near the
equator, where the Coriolis term is small there is no geostrophic balance. Also, friction and
curvature in the isobars provide important steering mechanisms.
Friction is an important force
form motions within the boundary
layer; where frictional drag of the
surface affects motion. Friction acts
in the opposite direction of motion,
tending to decrease the speed thus
decreasing the Coriolis force. A new
balance between forces is created,
where the pressure gradient force is
balanced by the vector sum of the
frictional and Coriolis forces. Under
such a balance, the parcel of air drifts
slowly towards the lower pressure region. In general, as one increases height above the surface, the
frictional drag decreases and the angle between the winds and the isobars decreases.
Under conditions of curvature in isobars, another steering force comes into play: centripetal
force. Under conditions of curved isobars (ie: circular motion), a component of the inward directed
force must provide the centripetal force for the parcel to follow the isobars. For a low pressure cell,
the pressure gradient force provides the centripetal acceleration and the Coriolis force balance what
is left. For a high pressure cell, the opposite occurs. As a result, the wind velocities around a low
pressure centre are lower (known as subgeostophic flow or cyclonic flow) than around a high
pressure centre (known as supergeostrophic flow or anticyclonic flow).
1.1. Westerlies
One consequence of geostrophic flow is that at most latitudes (except at the poles and near the
equator), the airflow in the middle and upper troposphere is westerly. The reason for this is shown
in the diagram below. At southern latitudes, where temperatures are higher, the air is less dense.
As a result, the rate of pressure decrease with height is less than the in northern latitudes. This
results in a horizontal pressure gradient aloft. Under a condition of geostrophic flow, the winds will
Lecture 13, Page -2-
blow from the west. (The same logic can be used in the southern hemisphere to explain the westerly
flow).
2. Convergence and Divergence
Most meteorological charts show pressures and wind speeds and directions on horizontal plane.
This shows the horizontal flows but says little about vertical motions of air. Any flow towards a low
pressure centre is known as
convergence. An example is air
flow into the centre of a cyclone.
Divergence occurs when there is
an outflow of air from a region of
higher pressure, such as from an
anticyclone. In general, if air is
converging at the surface, then the
air must be rising and diverging at
the top of the troposphere.
Similarly, if air is converging at
the top of the troposphere, then air
must be sinking and diverging at
the surface.
3.
Scales of Motion in the
Atmosphere
All circulations are caused by regional temperature differences which arise from un even heating of
the earth’s surface by the Sun. The scales of this circulation is highly variable but is organised into
patterns of varying sizes and life-spans. The scales of these motion are summarised in the following
table:
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Planetary
weeks to years
1000 to 40000 km
trade winds
Synoptic
days to weeks
100 to 5000 km
cyclones, anticyclones,
and hurricanes
Mesoscale
minutes to days
1 to 100 km
land-sea breeze,
thunderstorms, tornadoes
Microscale
seconds to
minutes
< 1 km
Turbulence, dust devils
and gusts
Macroscale
Lecture 13, Page -3-
3.1. Mesoscale Circulation
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Mesoscale winds or local winds are small scale
winds which are generated by local uneven heating
of the Earth. One example of such a wind is the
land-sea breezes. Such breezes are created by
temperature differences between the land a sea
surfaces at different times of day. In the morning
under calm conditions, there is little temperature
difference between the land and sea surfaces
resulting in no pressure gradient between the land
and sea surfaces. As the day proceeds, the land heat
quicker than the sea resulting in a horizontal pressure
gradient between the land and sea. (The sea does not
heat as fast as land because of different water has a
higher albedo and the heat that is absorbed can be
transported away by currents). This results in a
circulation pattern where are rises over land and
descends over the sea.
This circulation is
characterised by a breeze coming inland from the
sea; sea-breeze. At night, the land cools by radiative
cooling and the sea cools very slowly (due to currents
in the water transporting heat). The results in a
reversal of the circulation pattern and winds blowing
out to sea; land-breeze.
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3.2. Macroscale Circulation
One of the first attempts to explain global circulation
patterns was made by George Hadley in 1735. Hadley
proposed that the large temperature variation between the
poles and the tropics would produce a circulation pattern,
shown to the left,
that was similar to
the land-sea
breezes. In the
strong heated
tropical regions,
the air would rise
a n d
m o v e
p o l e w a r d .
Whereas polar air would sink and move equator-ward,
setting up a circulation cell known as the Hadley cell.
Although the model was correct in principle, it was later
Lecture 13, Page -4-
found to not fit the observed global pressure distributions and was replaced by another model. It did
not fit observations for a number of reasons including the effects of the Coriolis force, and friction
between the surface and the winds.
In the 1920's, a three cell
hemispherical model of
atmospheric circulation was
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proposed to fit observed data.
The figure to the right shows
this model along with the
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surface winds. The first cell
is locates in the zone between
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approximately 0( and 30(
latitudeand if often called the
Hadley Cell. Because of the
Coriolis force, winds tend to
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be easterly. In the middle
cell, surface flows tends to be
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poleward and the Coriolis
force results in a general
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westerly flow.
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Lecture 13, Page -5-
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Lecture 13, Page -6-
Appendix: Sample Questions
1) How might have Macroscale circulations effected the first European explorer who discovered
North America?
2) Calculate the geostrophic winds at a level of 70 kPa at a latitude of 60( with isobars at right
angles to meridians and a horizontal pressure gradient of 0.1 kPa per ( latitude.
Lecture 13, Page -7-
Lecture 14: Atmospheric Dynamic III
1. Jet streams
Embedded in the westerly flow of the
mid-latitudes, is high speed streams
of wind known as Jet Streams. These
streams, which occur just below the
tropopause, are narrow (1 to 2 km)
and wide (100 to 500 km). Wind
speeds at the centre of the jet are
typically 125 km h-1, but can reach up
to 500 km h-1. The source of these
jets is the temperature contrasts on
the surface producing pressure
gradients aloft. During winter periods the
horizontal temperature variation on the
Earth’s surface may be very large over a
small distance. This results in large pressure
gradients aloft and strong geostrophic flow.
In the mid-latitudes, large temperature
gradients are often associated with the polar
front. The frontal region is associated with
the convergence of the cold polar easterlies
and the warmer westerlies. The jet that
results is known as the polar jet stream. This
stream varies seasonally, moving further
south and becoming stronger during the
winter season (due to greater temperature
gradients in the winter caused the expansion
and strengthening of the polar vortex). It also
varies over shorter time scales with waves
pushing the jet north and south. Taken together, the polar jet stream migrates between 30( and 70(
latitude and , as such, is often called the mid-latitude jet stream.
The jet stream plays an important role in determining the weather. It provides energy to the
circulation of surface storms and also directs their paths of movement (mid-latitude low pressure
cyclones often follow the jet stream). Consequently, observation of the jet stream is an important
component of modern forecasting.
2. Atmosphere - Ocean Interaction
The atmosphere and ocean do not act as separate systems, but can influence each other. Oceans
cover the majority of the planets and at their point of contact, energy is exchanged between them.
Unlike land, however, ocean circulations move vast amount of energy within the Earth-atmosphere
system. Also, friction between the winds and the ocean surface provides a drag force which tends
to drive the ocean circulation. In equatorial regions, the ocean currents tend to be easterly
corresponding to the easterly trade winds. In the mid-latitudes, the currents tend to be westerly. Like
the atmosphere, the circulation of the oceans are also effected by the Coriolis force, resulting in
circular current patterns which are found in every major ocean basin. In the north Atlantic, a portion
of the equatorial current is deflected north by the prevailing westerlies. The stream, known as the
Gulf Stream, transfers energy towards Europe, keeping it relatively warm for its latitude.
In addition to driving surface currents, winds can also drive the upwelling of deeper, colder
water. This effect is most known on eastern coasts, such as California. The equator-ward motion
of the ocean tends to draw water up to replace water the has moved.
3. Air Masses
Regional weather patterns are often
strongly influenced by the motions of large
bodies of air called Air Masses. Air masses
are large bodies of air which are
characterised by source regions and
homogeneous physical properties, such as
humidity and temperature. When these air
masses move out of it region of origin, they
effect the weather in other regions.
Lecture 14, Page -2-
Air masses are classified by there source regions, depending on the latitude and nature of the
source region. Classification and identification is by a two letter code making reference to the
latitude {polar (P), arctic (A), tropical (T), and equatorial (E)} and to surface type {continental (c)
and maritime (m). The characteristics of North American air masses are listed below:
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3. Weather Patterns
In the mid-latitudes, the primary weather
producing systems is the mid-latitude cyclone.
These cyclones are large low pressure regions
which travel eastward and last for periods of days
to weeks. They are characterised by a counterclockwise circulation. They most often have
associated with them both a cold and a warm front
a extending from a central area of low pressure.
Forced frontal lifting of air results in cloud
development and precipitation. The circulation
often results in a comma shaped cloud pattern.
3.1. Fronts
Fronts are boundaries between separate contrasting air masses and are usually characterised by rapid
changes in temperature and humidity. On weather maps they are represented by lines showing the
interface at the surface (except in the case of occluded fronts). Above ground, the front slopes at an
angle with warmer less dense air rising over the cooler more dense air.
Lecture 14, Page -3-
3.1.1 Warm Fronts
A warm front occurs when warmer
air displaces cooler air. As the cooler
air retreats, friction with the ground
greatly slows the motion at the
surface. Consequently, the warm
front forms a shallow wedge with an
angle of approximately 0.25( to 0.5(.
As the warm air pushed over the front
slowly rises, it expands and cools
often forming clouds and sometimes
precipitation, even in stable
conditions. Due to the slow rate of
ascent, the cloud form are usually
middle to high levels clouds, such as
nimbostratus, altostratus, and cirrus. The typical velocity of a warm front is about 25 km h-1.
3.1.2. Cold Fronts
A cold front occurs when colder air displaces warmer air. As the warmer air retreats, it is
wedged up above the more dense cooler air. Cold fronts typically have a slope of approximately 1(
and a typcial velocity of about 35 km h-1. The due to the speed of the fronts movement and the angle,
the forced lifting of warm air often causes the rapid release of latent energy in the warm air, which
greatly enhances its buoyancy and precipitation intensity. Sometimes cold fronts can result in violent
weather and sharp temperature changes.
3.1.3. Occluded Fronts
Occluded fronts occur when a cold front over runs a warm front, due to differences in fronts
speeds. The advancing air wedges all the warmer air aloft.
3.2. Life Cycle of the Mid-latitude Cyclone
The idealised life cycle of a mid-latitude cyclone is as follows:
a) The two air masses of differing temperatures and densities are moving parallel to each other
in opposite directions. This provides an interface with shearing forces.
b) The shear between the air masses starts a cyclonic motion producing a region of low pressure
and warm and cold fronts.
c) The deepening of the low pressure region resulting in the classic mature mid-latitude
Lecture 14, Page -4-
cyclone.
d) The difference in speeds of fronts results in the occlusion of the fronts and the lifting of the
warm air mass.
Lecture 14, Page -5-
3.3. Cyclogenesis
Upper airflow is important in the
development of cyclonic and
anticyclonic motion. Early in the
h i s t ory of u p p e r - a i r f l o w
measurements, it was discovered that
the position of mid-latitude pressure
systems were often dependent on the
position and meanderings of the polar
jet. It was noticed that where a
“ridge” results in anticyclonic motion
and a trough results in a cyclonic
motion. Such surface activities tend
to be stronger during the winter when
the polar jet tend to wander north
and south more. It was also noticed
that in regions of upper air
convergence and divergence also
induced cyclonic (and anti-cyclonic)
motions. Consequently, surface
cyclones (and anticyclones) tend to
form directly under the jet, and
follow the motions of the jet.
Lecture 14, Page -6-
Appendix: Sample Questions
1) Although the formation of the occluded front represents the period of maximum intensity of
cyclone, it also marks the beginning of the end of the system. Explain why.
2) Describe the weather an observer would experience if the centre of a cyclone passed to the north.
3) Why is predicting upper level airflow important in modern weather forecasting?
Lecture 14, Page -7-
Lecture 15: Atmospheric Optics
Acknowledgements:
Image/Text/Data from the University of Illinois WW2010 Project.
http://ww2010.atmos.uiuc.edu/
1. Atmospheric Optics
Atmospheric Optics refers to optical phenomena caused the interaction of Sun light with particles
in the atmosphere. The most common types of atmospheric particles are liquid water droplets and
ice crystals. The optical interactions that occur include refraction, reflection, scattering, and
diffraction.
1.1. Optics of Atmospheric Liquid Water
Droplets
One of the most commonly observed
atmospheric optical phenomena is the
rainbow. Rainbows result from refractionreflection-refraction process of Sun light
passing through water droplets. Light that
enters the droplet is refracted. However, the
angle of refraction is dependent on the
wavelength of the light. Blue light is
refracted (bent) more than Red light. The
light passes through the droplet till it hit the
back of the droplet, where some of the light is
reflected. If the angle of incidence is greater the 48(, then all the light is reflected. The light that
leaves the droplet emerges at angles between 40((blue or short wavelength) and 42( (Red or long
wavelength) of the incoming beam. If enough
droplets are in the sky, then the
intensity of this refracted light is
enough to see a rainbow.
1.1.1. Secondary Rainbows
On very rare occasions, a
secondary rainbow can be observed.
They occur due to a two reflection
process. Instead of one rainbow, two
are seen; the second at a larger angle from the antisolar point. The due to increased reflection losses,
the secondary rainbow is not as intense as the
primary. Also, the colour scheme of the secondary
bow is the opposite of the primary.
1.2. Optics of Atmospheric Ice Crystals
In the wintertime, we no longer see rainbows.
This is because water droplets have been replaced by ice crystals.
These crystals have specific shapes of which two common shapes
are six sided columns and plates. (Both crystals are essentially the
same shape, with the columns having a longer third axis). The
interaction of Sunlight with these crystal produce a wealth of optical
effects including, haloes, arcs and spots.
1.2.1. Refraction Through Ice Crystals
Sun light can be refracted by passing through ice crystals.
The angles with which the light is refracted are dependent on
which surfaces od the crystals the light passes through. If
light passes through two
of the hexigonal surface
of a crystal (bottom
right), then the
minimum deflection will
be 22(. It light passes
through one of the
hexagonal faces and out
on of the perpendical
Lecture 15, Page -2-
faces, the minimum deflection is 46(. Each of these deflections can
result in an atmospheric optical effect.
The refraction of light
through two faces of the
hexagonal crystal results in
two possible optical
phenomena. The first is a
22( halo around the Sun.
This is a result from
randomly oriented ice
crystals 22( away from the
Sun refracting light towards
you, the observer. The
second effects results from
the non-random orientation
of plate ice crystals. Falling
plate crystals in still air tend
to fall with a perpendicular
face down. This results in
bright spots to the left and
right of the Sun at 22(,
called Sun Dogs.
The refraction of light
through one of the
hexagonal faces and one of the perpendicular faces results in a
similar halo, except at 46(. This results in a very large halo,
with a total angular extent of 92(.
1.2.2. Reflections Off Ice Crystals
Reflections off the surface of ice crystals also result in
some interesting optical effects known as pillars. Pillars
result from single reflections off the surfaces of crystals.
Consider, for example, single reflection off the
Lecture 15, Page -3-
perpendicular surface of plate crystals when the Sun in low
to the horizon. If the wind conditions at low, then these
crystal will fall generally oriented with the largest face down.
Reflection off of the perpendicular surfaces results in pillars
of light extending above and below the Sun.
1.3. Atmospheric Refraction
The Earth’s atmosphere is not of constant
density, of varies with height (pressure) and air
temperature. As such, light travelling through the
does not travel in s straight line, but is refracted as it
moves into regions of changing density. This results
in a phenomenon known as mirages.
Consider a case of looking out at a boat in a lake.
The lake is usually cooler than land and the air
closest to the lake is often cooler than the air above.
As a result a temperature inversion can occur causing
the light rays to be bent downwards. The apparent image of the boat is elevated, and in known as
a superior mirage. Sometimes this effects allow one to see things that either over the horizon or
blocked by other object. (Note is effect is sometime not so noticeable. This is because, not only the
boat is elevated, but so is all the water between the boat and the observer).
A second type of mirage is known as a desert mirage or inferior mirage. Such mirages often
occur in deserts when the air at the surface is very hot, but cools rapidly with height. This results
in increased refraction as light passes closer to the ground. This can result in the inversion of an
object in the distance. Such mirages can sometime be seen on highways, where an image of a car
in the distance appears below the car.
Lecture 15, Page -4-
Lecture 16: The Stratosphere
1. Structure of the Stratosphere
The Stratosphere is a region of the
atmosphere wh i ch ex tends from
approximately 10 to 50 km altitude and is
characterised by region of increasing
temperature with height. This gradient
strongly inhibits vertical motions and is
therefore very stable (or stratified). Since
there is very little vertical mixing, it remains
close to radiative equilibrium. It radiative
budget is dependent on the absorption of
incoming solar radiation (primarily in the
UV), and the emission of infrared radiation
(primarily by CO2). The thermal structure is
determined by the distribution of ozone (O3).
Due to the variation in latitudinal heating and
the geostrophic balance, the majority of the
motion of the stratosphere is zonal (eastwest), with only a small meridional
component to transfer heat.
1.1. Ozone Photochemistry
The first treatment of stratospheric O3
chemistry was by Chapman in 1930. He
considered the formation of Ozone by the
photolysis of oxygen into atomic oxygen followed by a three-body reaction to form ozone:
O 2 + hν → O + O
O + O2 +M → O3 +M
The photolysis of ozone requires UV radiation of wavelengths of 242 nm or shorter. Ozone could
the be destroyed by reaction with atomic oxygen or by photolysis by UV radiation 310 nm or shorter.
O 3 + O → 2O 2
O 3 + hν → O 2 + O
Lecture 16, Page -1-
The plot to the right shows the
theoretical Chapman profile and the
observed tropical and extra-tropical
concentrations.
O3 production
peaks in the mid-stratosphere near
30 km, below which decreases due
to the extinction of UV in the solar
beam above.
1.2. Involvement of Other Species
Other atmospheric species tend to
disrupt the destruction processes of
stratospheric ozone. The classic
process is the chemical catalytic
destruction cycle:
Lecture 16, Page -2-
R + O 3 → RO + O 2
RO + O → R + O 2
R + O 3 + O → R + 2O 2
where R is a radical such as Cl or NOx. In this cycle, the radical can continue on to destroy more O3
molecules. These radicals are removed by reaction with other species into an inert form (for Cl,
reaction to form HCl and ClONO2). Human activities can have a large impact on the chemical
makeup of the stratosphere. A classic example of this impact is the Southern hemisphere ozone hole.
(Note: The Ozone total column is expressed in Dobson Units. 1 DU is the depth the O3 column
would assume, in thousandths of a centimetre, if it was brought to standard temperature and pressure.
ie. 400 DU = 4 mm).
Lecture 16, Page -3-
Lecture 16, Page -4-
1.3. Formation of the Hole
Until the discovery of the O3 hole in the Antarctic, it was widely believed that Cl did not play a
major role in the destruction of O3 in the stratosphere. It was thought that most of the Cl was locked
up in one of the two Cl reservoir species (HCl and ClONO2). However, upon the discovery of the
O3 hole, a new understanding of the processes involved had to discovered.
The O3 hole begins to form during the Southern hemisphere winter. When the pole is plunged
into darkness, the stratosphere begins to cool. A circulation known as the polar vortex begins to
extend up above the level of the tropopause (due to the cooling) and prevents the mixing of
stratospheric air between the inside and outside of the vortex. Also, the temperatures drop low
enough for ice clouds to form in the polar stratosphere (Polar Stratospheric Clouds, PSCs). On these
clouds, HCl and ClONO2 condense, and in the heterogeneous phase they react, releasing large
amounts of gaseous Cl2. Over the winter, the Cl2 builds up in the stratosphere. In the spring, when
the Sun returns to the polar region, the Cl2 is quickly split into atomic Cl and begins to catalytically
destroy O3. Due to the amount of Cl in the stratosphere, O3 is almost completely destroyed before
the breakup of the polar vortex, leaving an O3 “hole” over the South Pole.
Appendix: Websites
TOMS: Total Ozone Mapping Spectrometer:
http://jwocky.gsfc.nasa.gov/
GOME: Global Ozone Monitoring Experiment
http://auc.dfd.dlr.de/GOME/
Lecture 16, Page -5-