Lecture 1: Composition and Structures in the Atmosphere

1. Composition of the Atmosphere

i). Principle Gases

Permanent Constituents Variable Constituents

ConstituentFraction byVolume

ConstituentFraction byVolume

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)* 100 ppbv

Neon (Ne) 18.18 ppmv Sulphur Dioxide (SO2)* 100 ppbv

Helium (He) 5.24 ppmv Nitric Oxide (NO)* 0.5 ppbv

Methane (CH4)* 1.7 ppmv Hydrogen Sulphide (H2S)* 0.05 ppbv

Krypton (Kr) 1.14 ppmv Nitric Acid (HNO3) Trace

Hydrogen (H2) 500 ppbv Chlorofluorocarbons CFCl3, CF2Cl2, CH3CCL3,

CCl4Trace

Nitrous Oxide (N2O)* 300 ppbv

Xenon (Xe) 89 ppbv Hydroxyl (OH) 10 pptv (daytime)

Carbon Monoxide (CO)* 80 ppbv

*Concentrations at the Earth's surface.

Lecture 1, Page -2-

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 anddynamical) vary with height. This is observable by the manner in which temperature and pressurechange with height.

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2.1. Vertical Temperature Structure: The Atmosphere has traditionally been separated into fourdistinct regions on the basis of the temperature profile. (However, there are no impenetrable surfacesbetween 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 - region of decreasing temperature with height- between stratopause (�50 km) and mesopause (�80 km)- coolest region of atmosphere

iv). Thermosphere - region of increasing temperature with height due to absorption ofshort 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 surfaceexposed to a gas (N m-2 or Pa). The force is exerted by collisions of gas molecules with the surface.

Consider: a) Pressure versus Temperatureb) Pressure versus Density

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P R T= ρ *

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 - PTemperature - TDensity - '

These are related by the equation of state (ie: the ideal gas law):

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 adjuststo a state of “Hydrostatic Equilibrium”. The downwards force due to gravity on air is balanced bya pressure gradient force.

Consider a volume of air of thickness dz and area dA:

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( ) ( )dP z z g dz= −ρ

( ) ( ) ( )dP z g z dz

P zR T

g dz= − = −ρ *

( )( )

dP zP z

gR T

dz= − *

( ) ( )dP zdz

z g= −ρ

dPP

gR T

dzZ

P

P z

= −∫∫ *( )

( )

00

P z P z H( ) ( ) exp( )= −0

Under this condition of balance, the variation of pressure in the atmosphere with height can be

expressed by the “Hydrostatic Equation”:Thus, decrease in pressure through a thin layer of thickness dz is:

To determine the pressure as a function of height in the static atmosphere, integrate thehydrostatic equation:

- substitute for density (using the ideal gas law):

- rearrange:

- integrate from ground-level to a height Z:

- rearrange:

Lecture 1, Page -6-

where: , the scale heightHR T

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 daytimeconcentrations (in molecules per m3) of OH. If the average lifetime of the a OH molecule is 0.1seconds, what is the daytime rate of production of OH (in molecules per m3 per hour)? Assumingthat each OH molecule is created by the photolysis of a water molecule, what mass of water isdestroyed (kg per m3 per hour).

2) Altitude sickness is a common problem for people when they reach altitudes over 4000 m abovesea level. Using the hydrostatic equation and assuming that the atmospheric Temperature is constantwith height at 10(C and the sea surface pressure is 101.325 kPa, calculate the pressure at thisaltitude.

3) What is the total mass of the atmosphere?

4) Assuming an incompressible atmosphere with a temperature of 15(C, what height of atmospherewould 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 100kPa, 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 bykilling himself/herself in the most extraordinary way. The 1997 Award went to Larry Water of LosAngeles (who survived his award-winning accomplishment). He purchased 45 weather balloons andseveral tanks of helium, inflated the balloons, attached them to a lawn chair and tied himself to thechair. When he cut the cord attaching the chair to his jeep he shot up into the air and didn’t stopclimbing until about 11,000 feet. He was rescued by a helicopter but immediately arrested forviolating 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 flightwas 100 kg. Assume that the surface temperature was 25(C and the “cruising” altitude temperatureand pressure was 3(C and 67 kPa, respectively. Estimate the initial and final diameters of theballoons at Larry’s “cruising” altitude of 11,000 feet. Identify all the assumptions that were madein coming up with your answer.(Just in case you don’t believe me, see: http://www.officialdarwinawards.com/index.html)

F T= σ 4

λ m ax =aT

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 becharacterised by wavelength, frequency, amplitude, and energy . All EM wave travel at the samespeed; “the speed of light”, which is 2.998 × 108 m s-1 in a vacuum. There exists an entire spectrumof 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 ofthe EM spectrum. The human retina is sensitive to wavelengths ranging from 0.7 µm (red) to 0.4µm (violet). Human Skin can detect infrared radiation as heat. Within the Earth’s atmosphere, EMradiation 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 radiationfrom the surroundings.• The properties of the emitted EM spectrum are almost independent of the material, but stronglydependent on temperature.• Properties of thermal radiation:

1. All objects emit radiant energy with a continuous spectrum - The Planck Spectrum2. 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):

where: 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, thethe wavelength of peak emission is (Wien’s Displacement Law):

Lecture 2, Page -2-

where: a = Wien’s Constant = 2897 µm K4. 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, thanthe object will receive more radiant energy (F = )T4) than it is emitting. This will cause the objectstemperature to rise until it reaches a new equilibrium at which absorbed and emitted energy isbalanced. 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 anequilibrium temperature of the object. Consider the Earth:

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E T Rs s s= ×σ π4 24

FER

TR

Rss

s es

s

s e

= =− −4 2

42

2πσ

F Rs eπ 2

F R As e eπ 2 1( )−

i. The Solar Input

Emission of Sun in all directions (Flux × surface area of Sun) (in W):

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):

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’satmosphere (Fs) times the Earth’s shadow area:

However, a fraction of the radiation incident on Earth will be reflected and/or scattered back intospace by clouds, molecules and the planet surface. The fraction of radiation that is not absorbedis called the “albedo” (A). The albedo of Earth (Ae)is approximately 0.30. (30% of incidentsolar radiation is lost to space). The total solar energy absorbed by the Earth is therefore:

In radiative equilibrium, this absorbed radiant energy will be balanced by emission of thermal

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E T Re e e= σ π4 24

F R A T Rs e e e eπ σ π2 4 21 4( )− =

TF A

es e4 1

4=

−( )

σ

radiation from Earth.

ii. Terrestrial Radiation

The rate that energy is emitted by the Earth is (in W):

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

Rearranging to determine the effective radiating temperature Te:

iv. Effective Radiating Temperature

What is the effective radiating temperature of the Earth? Consider the following data:Re = 6.378 × 106 m = 6378 kmRs = 6.599 × 108 mRs-e = 1.496 × 1011 mAe = 0.30Fs = 1360 W m-2

Therefore Te = 255 K = -18 (C

But the Earth’s average surface temperature is 288 K (or 15 (C). Why?

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Consider other Planets:

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 reachesspace. The atmosphere will then re-radiate this energy; some up to space, and some back down tothe surface. Then the effective outgoing flux from the planet will be from the atmosphere. Thus thelower levels of the atmosphere may have much higher temperatures.• The difference in temperatures between the surface temperature and Te depends on the opacity ofthe atmosphere to IR radation.• The following figure shows the fraction of terrestrial and solar radiation absorbed as a function ofwavelength. The atmosphere is moderately transparent in the visible region, so that much of thesolar radiation reaches the ground. However, in the IR, where terrestrial region emission peak, thereis 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 surfacetemperature must exceed Te.

Question: Can a planet’s surface temperature be lower than Te?

Planet AlbedoFs (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

Lecture 2, Page -6-

Appendix: Sample Questions

1) Why does the amount of solar energy received at the Earth’s surface change when the altitudeof 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 inthe Earth’s effective radiating temperature Te if the peak in the peak in the Sun’s spectrum shiftedfrom 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 radiatingtemperature 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 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 radiation2. 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 tovisible radiation but is opaque to IR. (This analogy breaks down because the glass of a greenhouseprovides a physical barrier to the motion of air and thus heat loss/transport due to convection. Thereis 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:

Lecture 3, Page -2-

E S R= +

F R E+ =

F S=

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. Eis the energy emitted by the Earth’s surface (infrared). R is energy emitted from the atmosphere thatis absorbed by the Earth’s surface. And F is the energy emitted upwards from the atmosphere. Itfollows that if the system is in steady state (not heating up or cooling), then the radiation emitted bythe surface must balance the energy absorbed:

Also, the energy emitted by the atmosphere must balance the energy absorbed by the atmosphere:

Also, the energy emitted at the top of the atmosphere must balance the energy entering theatmosphere:

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 theatmosphere. 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 moreinfrared energy. This would cause an increase in the temperature of the atmosphere, causing theERL to rise and increase the energy emitted by the atmosphere to the surface (R). This in turn wouldheat the surface until balance with the surface emission was achieved.

Lecture 3, Page -3-

Q A Q Y= + (1)

3. The Two-Tone Model

To demonstrate the green house effect, we can consider an atmosphere which is transparent to solarradiation and opaque to IR. In order to keep things simple, let us separate the atmosphere from thesurface of the planet, make the atmosphere a thin layer, and distribute the solar energy evenly overthe surface.

In radiative equilibrium, the upwards and downwards fluxes of radiation must balance; both at thetop of the atmosphere and at the surface.

The flux of radiation entering the atmosphere must be balanced by the amount leaving:

The flux of radiation on the planet surface must be balanced by the amount emitted by the

Lecture 3, Page -4-

T T K Kg e= = =2 2 255 3034 4 ( )

Q Y A Q X+ = + (2)

X Y= 2 (3)

Y Te= σ 4

X Tg= σ 4

surface:

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):

The flux of radiation from the surface is:

where Tg is the surface temperature.

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 ofclouds effect this model?

4) In the two-tone model described above, what is the value of Q? How is it related to the solarconstant Fs?

5) The two-tone model presented above makes a number of assumptions about the earth-atmospheresystem. A number of modifications to the model might be envisioned improve its accuracy. Someof these include:

a) What if the atmosphere was partially transmitting in the infrared tone?

Lecture 3, Page -5-

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 theeffective radiating temperature (Te) decrease?

b) Consider a two-tone model of the Earth. Calculate how many degrees would the surfacetemperature change if the solar constant were to decrease by 10%.

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 inputspread 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. Therest of this incident solar radiation (30%) is back-scattered/reflected back into space; 4% by thesurface, 20% by clouds, and 6% by air molecules. In total 19% of the incident solar radiation isabsorbed by the atmosphere, 51% by the surface and 30% is reflected/back-scattered into space (thealbedo).

In order to remain in an energy balance, 51 units of energy is emitted by the surface; 7 units ofsensible heat, 23 units of latent heat, and a net IR emission of 21 units (6 units of which are notabsorbed by the atmosphere but escape to space). Note that net IR emission represent less than halfof 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 and38 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 spaceoriginates in the atmosphere.

Lecture 4, Page -2-

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 Reflected / Back-Scattered 30

Atmospheric emission to Space 64

Surface emission to Space 6

Total 100 Total 100

Lecture 4, Page -3-

0

10

20

30

40

50

Sol

ar Z

enith

Ang

le

0 20 40 60 80 100 Number of Atmospheres

2. Variations in Solar Input

2.1 Latitude

We know from experience that the solar radiative input varies with latitude in daily and yearlycycles. These variations are a result of changes in the orientation of the Earth’s surface relative tothe 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 angleincreases, the amount of energy per unit area incident on the surface decreases. Also, at higher solarzenith angles, the solar radiation has to travel through more atmosphere. This provides moreopportunity for the solar radiation to be scattered away or absorbed before reaching the surface.

Solar Zenith Angle # of Atmospheres

0( 1.00

10( 1.02

20( 1.06

30( 1.15

40( 1.31

50( 1.56

60( 2.00

70( 2.92

80( 5.70

85( 10.80

90( 45.00

Lecture 4, Page -4-

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 -5-

F TR

Rs ss

s e

=−

σ 42

2

F FR

Rs s

s e

s e

′ = ′

−

−

2

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 Sunbeing approximately147.5 × 106 km and 152.5 × 106 km. Remembering that the solar constant isinversely proportional to the distance between the Sun and Earth (Rs-e):

This eccentricity results in a variation in the Solar constant of approximately ±3% :

Eccentricity plays a only minor role in seasonal variations. In fact we are nearest the Sun aroundJanuary 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 resultof changes in the solar zenith angle and length of day, caused by the fact that the Earth’s rotationalaxis is not perpendicular to the orbital plane. The angle between the orbital plane and the axis ofrotation is called the “inclination ”. Since the axis of rotation does not change (always directedtowards the north star - Polaris), its orientation relative to the Sun’s rays changes throughout theorbit.

Consider three cases.1) Uranus has an inclination of nearly 90(:

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At one point in the orbit the north pole point toward the sun. The sun appears directlyoverhead at the north pole. The entire northern hemisphere is in continuous daylight whilethe 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 ofradiation throughout the orbit (year). Thus there are no seasonal variations. Solar inputvaries only with latitude.

3) Earth has an inclination of 23.5(:

Lecture 4, Page -7-

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 southernhemispheres receive, resulting in the seasons.(Note: Summer Solstice, Winter Solstice and the Equinoxes).

2.4 Solar Constant Variations

Lecture 4, Page -8-

The Sun is the primary source of energy responsible for governing both the weather and theclimate of Earth. For that reason alone one would expect that changes in the amount of energy Earthreceived 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 welldocumented. The variations in solar flux are generally cyclic with times ranging from the 27-daysolar rotation period, through the 11-year and 22-year solar activity periods, to very long cycles ofhundreds to thousands of years duration.

Much meteorological and climatic data suggest that there are significant responses in Earth’satmosphere and oceans to variability on the part of our Sun. Drought cycles, variations in global seasurface temperatures, variations in stratospheric temperatures at specific locations, variations in thetracks followed by storms across the Atlantic, variations in year-to-year tree growth as determinedby tree-ring studies, and climate variations exposed by glacial ice-core studies have all shownremarkable correlation with various forms of solar variability over time spans ranging up to 100,000years.• 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 ofatmospheric responses to changes of these time scales.

• 10.5 Year Solar Cycle: The most prominent period observable is that of the "Solar Cycle". It hasbeen observed in Chinese sunspot records dating back two thousand years. Many of theobserved changes in climate are correlated with 10.5 year solar cycle period. It has been shownthat the tracks of storms across the oceans change in latitude with changing phases of the solarcycle. These changes in storm tracks could be the cause of droughts and floods which showperiodicities 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 upin ice core records and tree ring records that can be taken back thousands of years. These periodsare still the subject of ongoing research. The confluence of these cycles have produced climaticchanges. The most recent dramatic example of this occurred in the 17th century during whichtime, the sun went several decades without sunspots. This period of solar minimum is referredto as the Maunder minimum and the climatic changes associated with this period include severecold in Europe with snow in the middle of summer. In more recent times, it has beenhypothesized that between 10 and 40 percent of the increase in the Earth's temperature over thelast 100 years (global warming) could be due to an increase in the solar flux associated with thesuperposition of several long-period solar oscillations.

• 23,000, 42,000 and 100,000 year cycles: Over long periods of time (thousands of years) the orbitof the earth around the sun changes due to many factors including the gravitational pull of otherplanets. The changes in the orbit will change the amount of solar radiation that the earthreceives. These variations cause major changes in the climate which cause long periods ofcooling. These periods of glaciation of much of the Northern hemisphere, referred to as IceAges, have been well documented to have occurred regularly over millions of years and theagreement between the Earth orbit around the sun and the Ice Ages is quite good.

Lecture 4, Page -9-

2.5 Volcanoes

Volcanoes have an immediate impact on the climate of the Earth and are noted to cause short-term 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 -10-

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 spreadaround the globe. These particles (primarily H2SO4 droplets or sulfate aerosols), tend to scatterincoming 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 ofthe atmosphere which will pass through the atmosphere and reach the surface), measured at theMauna Loa Observatory, Hawaii:

Lecture 4, Page -11-

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, Hawaiihttp://www.cmdl.noaa.gov/star/mloapt.html

iii) Today’s solar image:http://www.sec.noaa.gov/today.html

iv) The Big Bear Solar Observatoryhttp://www.bbso.njit.edu/

Appendix: Sample Questions

1) Given the latitude of Toronto, 43.7(N, calculate the daily average solar energy reaching thesurface on equinox, summer solstice and winter solstice. How many time longer is the atmosphericpaths on these days?

2) By how much does the solar constant vary over the year due to the Earth orbital eccentricity?

Lecture 4, Page -12-

3) Describe the seasons on Uranus. Saturn.

4) Describe the seasons if the Earth’s axis were inclined 40(. Where would the tropics of Cancerand Capricorn be located? How about the Arctic and Antarctic circles?

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 radiatingtemperature (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 H2Ovapour. However, human activities do not directly effect the amount of H2O vapour in theatmosphere. 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 theenergy distribution itself, will change our climate. In order to understand Global Warming, it isimportant 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 periodsare examples. Some changes are global in scale, while others have been regional or hemispheric.

Lecture 5, Page -2-

There are a number of natural factors which contribute to changes in the Earth's climate over varioustime scales. It is important to understand these factors when attempting to detect a human influenceon climate:

Changes in Solar Output: The amount of energy radiated by the sun is not constant. There isevidence in the temperature record of the Earth of an 11 year solar cycle (correlated to theSunspot cycle). Longer period changes may also occur. Changes in the Earth's Orbit: Slow variations in the Earth's orbit around the Sun modify thesolar 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 isabsorbed by the atmosphere before reaching space. The energy is then re-emitted by clouds andgases (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 naturalGreenhouse Effect as these gas species are naturally occurring in the atmosphereAerosols: These are very fine particles that are small enough to remain suspended in theatmosphere for considerable periods of time. They both reflect and absorb incoming solarradiation and absorb and emit in the IR. The type and quantity of aerosols in the atmosphere cangreatly 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 factorshave come into play affecting the Climate of the Earth.

Enhancing the Greenhouse Effect: Naturally occurring greenhouse gases (H2O, CO2, CH4, andN2O) keep the Earth warm enough to support life. Human activities release greenhouse gasesin large quantities. Principle in these activities is the burning of fossil fuels for the generation ofelectrical energy, heating and transportation. By increasing their concentrations and by addingnew greenhouse gases like CFCs, the greenhouse effect can/has be enhanced.

Land Use Change: As natural vegetation is replaced for agricultural use and asphalt, thereflectivity and IR emissivity of the Earth’s surface is substantially altered. These changes alsoaffect regional evaporation, and rainfall patterns (Latent heat fluxes). Aerosols: Humans add large quantities of aerosols to the atmosphere (both from agriculture and

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

Lecture 5, Page -3-

industrial activities). The effect on any global warming trends depends on the quantity andnature of the particles. However, regional effects can be significant.

Lecture 5, Page -4-

2.3 Radiative Forcing

As greenhouse gas increases in the atmosphere, the amount of infrared energy that is emitted to spacedecreases. The amount of decrease is the Radiative Forcing due to that gas. For example, radiativetransfer models have determined that if the CO2 in the atmosphere was doubled, the averageoutgoing infrared radiation would be reduced by 4 W m-2 from the present value of 237 W m-2 to 233W m-2. The projected radiative forcing of a number of greenhouse gases is shown in the followingdiagram (relative to the pre-industrial atmosphere).

Lecture 5, Page -5-

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 -6-

2.5 Climate Feedback Mechanisms

A climate feedback mechanism is a concept in which a property of the environment which ismodified by climate change will in turn affect the rate of climate change. A positive feedbackmechanism is a mechanism reinforces the climate change. A negative feedback mechanism tendsto 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 FEEDBACKb) 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 FEEDBACKc) 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 -7-

Clouds play a very large role in regulating the Earth’s environment. The net effects of cloudsis a very difficult problem since the scales involved ranges from less than 10-6 m to greaterthan 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 anextremely difficult task. This is due to the fact that the climate system is an almost infinitelycomplex system. In general, most climate models have predicted a global warming response toh u m a n a c t i v i t i e s( s p e c i f i c a l l y t h eanthropogenic emission ofCO2). The figure to theright show three scenarioso f g l o b a l a v e r a g et em p e r a t u r e ch an ge(adapted from “GlobalW a r n i n g . . . G l o b a lWarming” by M. A.Benarde, John Wiley,1992). The upper scenariobeing continued uncheckedemissions, and the lowerbeing curtailed emissions(from 1990).

Lecture 5, Page -8-

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 Laboratoryhttp://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 radiativeemission 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 emittedto space and, at the same time we say that the atmosphere remains in radiative equilibrium?

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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 masslessparticles which travel at the speed of light, c, and have an energy:

where: 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.

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 stateof greater vibrational, rotational, or electronic energy. The opposite may occur for emission of aphoton. IR photon are capable of inducing changes in the vibrational and rotational states ofmolecules. Shorter wavelength (higher energy) photons in the UV region are can cause electronictransitions and, in some cases, the dissociation of molecules (break them apart).

Each atom or molecule has itsown unique set of energy states andcan absorb or emit radiation only atwavelength corresponding totransitions between the energystates. Each molecule or atomtherefore has its own characteristicabsorption/emission spectrum.

The figure below shows thefractional absorption in theatmosphere as a function ofwavelength of a number ofradiatively important atmosphericgases. Each gas has a uniqueabsorption spectrum. O2 and O3

absorb mainly in the UV while H2Oand CO2 are the most importantabsorbers in the IR. It can also beseen that the atmosphere istransparent to much of the visibleregion. It can also be seen thatmuch of the terrestrial region isabsorbed by the atmosphere.

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Scattering is a process were an interaction between a photon and a particle results in a change ofdirection 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 sizeand density of scattering particles. In general, solar radiation is scattered in the Earth atmosphereby Rayliegh and Mie scattering

Lecture 6, Page -3-

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Scattering of photons by molecules, or molecular scattering, is commonly referred to as Rayleighscattering (named after Lord Rayliegh, who developed the theory). A significant property ofRayleigh scattering is that the efficiency of scattering is inversely proportional to the wavelength tothe 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):

If the flux of Red and Blue light were to enter a volume of gas, over five times more Blue would bescattered 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 whenflying on a jet? Check it out.......Red Sunset: When the Sun is on the horizon, the Sunlight travels through a much longeratmospheric path than when directly above. Much more of the shorter Blue/Green/Yellow lightis scattered away than Red before reaching the surface.

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 theatmosphere. If there is no exchange of heat between the parcel and the surrounding atmosphere, thenthe process is an “adiabatic process”.

The first law of thermodynamics states that the change in the total energy of a system equals thechange in the internal energy plus the work done against the surroundings. For the adiabaticprocess described above, since there is no change in the total energy, then the work done on theparcel of air equals minus the change in the internal energy.

E E Wtot = +in t = 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 LapseRate” (). 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 haveto be adiabatic, however the netchange in the total energy must bezero: ∆ ∆ ∆E E EA B C+ + = 0By determining the energy transferredat each stage (�E) and summing tozero, we will determine theAdiabatic Lapse Rate (). Forsimplicity, let us consider 1 kg of airbeing displaced.

Stage 1: Cool parcel to atemperature of 0 K. (This is notpossible, but remember this is only athought experiment). The amount ofenergy required to change thetemperature of 1 kg of air by 1(C isthe specific heat capacity (c). At

Lecture 7, Page -2-

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(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:

Stage 2: At T = 0 K, the parcel is lifted from Z1 to Z2. There would be no expansion in thisprocess since the parcel is at absolute zero. The parcel only gains gravitational potential energy:

Stage 3: Heat is added to the parcel to increase the temperature to T2.

Now, in order for the displacement from Z1 to Z2 to be adiabatic, the change in energy over thethree stages must sum to zero.

Rearranging:

or:

For adiabatic vertical displacement, the temperature of a parcel of air will decrease at a rate ofapproximately 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 watervapour 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). Thenin a dry atmosphere (no condensation), the temperature will decrease at the adiabatic lapse rate, .

Lecture 7, Page -3-

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This decrease in temperature will occur independentof the temperature of the surrounding atmosphere.However, the rate of decrease in the temperature ofthe surrounding air will determine whether theparcel will continue to rise or descend.

2.1 Buoyancy

Consider a small cylinder of air (shown to theright). If the air does not move in the vertical thenthe gravitational and pressure gradient forces mustsum to zero:

If a parcel is warmer than its surroundings it will also be less dense (ie. Lighter). The upwardpressure gradient force (which is associated with the surroundings) would be larger than thedownward 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 verticalmotions (convection), we will look at each case separately.

Case 1: Stable Atmosphere: In this case the environmental lapse rate is less than the adiabaticlapse rate. A parcel which is displaced upwards from point “A” will cool at the adiabatic lapse rate

Lecture 7, Page -4-

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(-10(C km-1). Since the temperature of the surrounding air is decreasing not as quickly, thedisplaced air will be cooler. The buoyancy will force the displaced air back towards its originalposition at point “A”. If the parcel is displaced downwards, it would be warmer than thesurroundings and buoyancy would push it back up.

Case 2: Unstable Atmosphere: In this case the environmental lapse rate (�) is greater than theadiabatic 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 convectionoccurs. This is referred to as convective instability.

Convection is common near the ground on sunny days. Solar radiation warms the ground andthe air near it (by conduction). This will greatly increase the environmental lapse rate �. Theheating 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 wherethe temperature has dropped low enough for water vapour to condense, then cumulus clouds mayform. However, once condensation occurs, latent heat is released into the parcel, changing theadiabatic lapse rate.

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 energybudget/climate since heat is released or absorbed during the phase changes. This is referred to aslatent heat.

A familiar experience involving latent heat is the melting of ice in water. The temperature ofthe water-ice mixture remains at 0(C until all the ice has melted. All the energy absorbed goes into

Lecture 7, Page -5-

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the disrupting the ice crystal structure of the ice. During the freezing process, the same amount ofenergy must be removed. The process of evaporation of water also requires an absorption of heatsince the molecules need extra energy to escape the liquid surface. This is why we sweat in orderto lower our body temperature. During condensation the same amount of energy is released. Twoother 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 whichis due to water molecules only. To a good approximation, water vapour behaves as an ideal gas:

where 'v is the vapour density and Rv is the specific gas constant of water vapour (461 J kg-1 K-1).

Saturation Vapour Pressure (es): Saturation occurs when the rate that molecules are leavingthe surface is balanced by the rate of molecules returning. As the temperature increases, the rate ofevaporation or sublimation will increase. Thus the saturation vapour pressure must increase withrising temperature.

Relative humidity (RH): This is the ratio of the actual amount of water vapour content to theamount required for saturation at the temperature of the air. It indicates how near the air is to beingsaturated. It can be expressed using the ratio of vapour pressure to saturation and is often expressedin percent:

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The following diagram is a phase diagram of water. Saturated vapour pressures are given by theline XTY’ for water and TY for ice. Water vapour is in equilibrium with either water or ice alongthese lines. The line TZ is the division between ice and water. If the state does not lie on one of thelines, then the system is not in equilibrium and will, in time exist in only one phase. Consider airthat is chilled from point “C” to point “B” (reduced temperature). This decrease will causecondensation. However, if there is no surface for the water to condense onto, then condensation maytake some time. As a result the air will be supersaturated.

Lecture 7, Page -7-

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 (condensedwater).

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 overice 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 relativehumidity? If the temperature increased to 30(C what would the relative humidity be?

Appendix: Saturation Vapour Pressure

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Lecture 8: The Ascent of Moist air

1. The Ascent of Moist Air:

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 withtemperature. 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 calledthe “Dew Point Temperature” (Td).

Generally a cloud is formed as a result of the adiabatic cooling associated with vertical liftingof moist air. As moist air ascends, its temperature will initially decrease at the dry adiabatic lapserate ( � -10(C km-1). At some height, the temperature will have decreased to the point wherecondensation into cloud droplets may commence. The height at which this occurs is referred to asthe “Lifting Condensation Level” (LCL). As the air continues to rise, its temperature will nowdecrease at the “Wet Adiabatic Lapse Rate” (�). This is smaller than the dry adiabatic lapse ratesince the latent heat released in condensation lower the rate of cooling.

In the example to theright, a parcel of air at(T,P,e) may be cooled atconstant pressure (or height)until e = es at the dew pointtemperature (Td). The liftingcondensation level (LCL)occurs at the intersection ofthe line with constant 100%RH (line B) and the dryadiabat extending upwardsfrom the initial position (lineA). Since the dew point andthe lifting condensation level(LCL) are related in thismanner, knowledge of eitherone is sufficient to determinethe other.

Now the conditions forstability are slightly differentthan before. For saturated air (condensation occurring), the wet adiabatic lapse rate is the criterionfor 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 lessthan the wet adiabatic lapse rate. Even when stable air is forced to rise above itscondensation level it remains cooler and heavier than the surrounding air.

The most stable conditions are when the temperature is increasing with height. The isreferred to as a “temperature inversion”. This frequently occurs at night near the ground as

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b) Absolute Instability: This occurs when the environmental lapse rate is greater than the dryadiabatic lapse rate. An ascending parcel of air will always be warmer and lighter than thesurroundings; both below and above the condensation level.

c) Conditional Instability: This occurs when the environmental lapse rate is less than the dryadiabatic lapse rate but greater then the wet adiabatic lapse rate (between about 5 and10(C km-1). A parcel of air would experience an upward buoyant force only after risingabove its condensation level, by some means other than convection. In this case theatmosphere is unstable only with respect to saturated air.

Absolutely Stable:

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Conditionally Unstable:

Lecture 8, Page -4-

2. Consequences of (In)Stability

2.1. Convective Clouds

Under unstable conditions (or conditionally unstable), a parcel of air may be pushed upward bybuoyancy. This typically occurs on a hot summer afternoon when solar radiation is intense and someareas of the ground are heated more than others. This typically occurs on a hot summer afternoonwhen solar radiation is intense and some areas of the ground are heated more than others (due tovariations in solar radiation absorptivities). As a parcel of air begins to rise, it will be pushed furtherupwards in unstable conditions. A cumulus cloud may form if the air rises above it liftingcondensation level (LCL). If the parcel is pushed even further upwards and if there is sufficientmoisture inthe air, then thismight result in a rain shower.Convective clouds areassociated with large updraftvelocities (1 to 30 m s-1) andare generally as thick orthicker in the vertical as theyare in the horizontal.

2.2. Stratus Clouds

Under stable conditions,convective clouds do notform. Although, there areother processes that can moveair vertically. The clouds thatform are generally of largehorizontal extent butvertically thin. Precipitationfrom these clouds is, at most,a light drizzle. Relativelysmall and localised updraftsof �10 cm s-1 may beassociated with such weathersystems with lateral extentsas large as 1000 km.

2.3 Temperature Inversions(and air pollution)

When Temperature isincreasing with height, it is

Lecture 8, Page -5-

referred to as a “temperature inversion” . The air is most stable in this case and thus most resistantto any vertical motions or mixing. The air near the ground level is cooler and heavier than aloft andtends to stay near the ground. This has important implications for air quality since pollutantsreleased 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. Sincethe ground is a more effective radiator than air, it will cool faster than the atmosphere. Also, sincethere are no clouds, surface emission is less likely to be trapped in the atmosphere. The air near theground 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 usuallypersist within valleys since colder air sinks from the uplands to the lowlands. Unfortunately, citiesand industry is often located in lowlands. Persistent temperature inversions enhance the problem ofpoor air quality.

Fog often forms when moist air cools and condenses near the surface at night and is trappedunder an inversion. If it were not for the inversions, the air would mix with drier air above andevaporate. This is why there is often a layer of fog in low lying areas in the morning after clear coolnights.

2.4. Changes in Stability (and thus weather)

1) Increase in Stability: Processes which cause temperature to decrease less rapidly or increasewith 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 decreasemore 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, andthunderstorms.

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 areadded to it at the surface. The air becomes unstable, generating clouds that produce heavysnowfall 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 isheated 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. Stabilityis also decreased by lifting when the lower portion of an air mass has more moisture than theupper portion. The lower portion will saturate and its temperature will decrease at the wetadiabatic lapse rate. This commonly occurs when moisture is trapped below the inversionlayer. For example:

Lecture 8, Page -6-

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Lift Layer A-B: Parcel at Areaches LCL immediately thencools at wet adiabatic lapse rate(�-5(C km-1). Parcel at B has tobe lifted at the dry adiabatic lapserate (�-10(C km-1) until itreaches its LCL. After that it willcool at the wet adiabatic lapserate. This can result in an airmass becoming unstable.

2.4.1. Lifting Processes

a) Orographic Lifting: As air flows overthe upwind slope of elevated terrain (suchas a mountain range), it coolsadiabatically as it ascends. This coolingmay generate clouds and precipitation. Clouds and precipitation are not likely to form downwind of the mountain since the air already lost much of its moisture and it warms adiabaticallyas 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 windscalled chinooks. Such winds are often created when a pressure system on one side of a mountainrange forces air over the mountains. As the air descends the leeward side of the mountain, it isheated 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 -7-

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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 suchaa can, the spay feels cold. Why?

2) Why does the adiabatic lapse rate of change when condensation begins? I have presented thatthe 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 orunstable.

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 mountainwas 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?

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Lecture 9: Formation of Clouds

1. Clouds

Clouds are composed of small spherical droplets of liquid water and/or ice crystals. These particlesare 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 cometogether. However, the saturated vapour pressure over a curved surface (such as a droplet) is greaterthan over a plane surface. Molecules are less strongly attracted to a curved surface and thusevaporate more readily. The excess vapour pressure (compared to that of a plane surface) requiredfor condensation to exceed evaporation (growth of a droplet) increases as the radius of the dropdecreases and its surface becomes more curved. A very large supersaturation will be required fora small aggregate of individual molecules to be in equilibrium and grow – otherwise it willevaporate. 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 dropcontains more than 105 molecules. These are not likely to come together by accident. In factsupersaturation in clouds rarely exceed 1%. Thus, embryonic droplets as large as 0.01 µm will notbe able to form by homogeneous nucleation. The mechanism for creating droplets with radius lessthan 0.01µm without large supersaturations is provided by aerosols. Aerosols which serve as nucleiupon which water vapour will condense to form a cloud droplet is known as a “CloudCondensation Nuclei”.

Lecture 9, Page -2-

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2. Atmospheric Aerosols

Atmospheric aerosols are small particles (solid or liquid) that are always present suspended inair. They range in size from 0.001 µm to over 100 µm radius and concentrations vary from 10-6 to107 particles per cm3. The particles are distributed throughout the atmosphere by turbulent mixingand 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 linesdue to breaking waves. There is a rapid decrease in sea salt aerosols when movinginland. These aerosols are very effective “cloud condensation nuclei” (CCN) since thedissolved salt is hygroscopic.

b) Crystals: Dust blown from ground and transported upwards by turbulence. The extremeweathering process on deserts provide preformed particles. Dry valleys generate mostof the crystal aerosols, although soils are also a source. Sand dunes have very fewparticles 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.

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Lecture 9, Page -3-

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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-to-particle 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

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 itcollides with on the way down.

b) Impaction on Surfaces: Aerosols can be lost by colliding with a surface, such as awindow.

c) Gravitational Settling: Settling out of the atmosphere is a significant loss mechanismfor particles of radius 1µm or greater.

Properties of aerosolsa) Wettable: A wettable aerosol is an aerosol that attracts water vapour. Hygroscopicb) Unwettable: An unwettable aerosol is one that avoids water vapour. Hydrophobic

Lecture 9, Page -4-

Adapted from: Wallace and Hobbs, “Atmospheric Science: An Introductory Survey”.

Lecture 9, Page -5-

Adapted from: Wallace and Hobbs, “Atmospheric Science: An Introductory Survey”.

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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 dropletincreases as the radius of the droplet decreases. This relationship is proportional to theinverse of the radius of the drop.

Solute Effect: Some of the aerosols in the atmosphere are soluble (ie. they will dissolve whenwater condenses on them. This causes the equilibrium vapour pressure surrounding thedroplet 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, thesmaller the droplet, the greater the solute effect. Thus the required saturation for growth ofdroplets to grow decreases as the radius of the droplet decreases. This relationship isproportional 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 equilibriumradius of a droplet has been derived, and is known as the Köhler Curve:

where (a/r) is the curvature term and (b/r3) is the solute term (a and b are constants). The plot to theright shows the shape of the Köhler curve for a particular drop. At small radii, the solution termdominates. Very small droplets can exist in equilibrium at relative humidities less than 100%. Ashumidity increases, the droplet willreach a critical saturation point (S*)where the drop will continue to growby condensation without furtherincrease in the saturation ratio. Thiscritical point also defines a criticalradius (r*). Below r*, droplets existin a stable equilibrium and will onlygrow with changes in the saturationratio.. Above r*, the curvature termdominates and the droplet willcontinue to grow until the saturationratio drops. Such drops are called“activated” and are CCN. In acloud, many droplets compete foravailable vapour and tend to lowerthe saturation ratio. Only a smallfraction of the atmospheric aerosolscan act as CCN: about 1% incontinental air and about 10% to 20%in maritime air.

Lecture 9, Page -7-

4. Nucleation of Ice Particles

Ice particles may form in air from the freezing of liquid droplets or by deposition directly fromvapour. 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 surfaceis 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 freezebefore such conditions were reached).

Ice crystals from by heterogeneous nucleation at temperatures above -40(C. However, icecrystals do not form readily on most particles found in air (not as readily as liquid water). The reasonis that molecules in ice are arranged in a highly ordered crystal lattice. If a foreign substance is toaid in the nucleation of ice, it must have a lattice structure similar to that of ice. The temperaturesat 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 -8-

Substance

Crystal Lattice Dimension Temperature toNucleate ((C) Commentsa axis (') c axis (')

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Ice 4.52 7.36 0

AgI 4.58 7.49 -4 Insoluble

PbI2 4.54 6.86 -6 Slightly Soluble

CuS 3.8 16.43 -7 Insoluble

CuO 4.65 5.11 -7 Insoluble

HgI2 4.36 12.34 -8 Insoluble

Ag2S 4.2 9.5 -8 Insoluble

CdI2 4.24 6.84 -12 Soluble

I2 4.78 9.77 -12 Soluble

Minerals

Vaterite 4.12 8.56 -7

Kaolinite 5.16 7.38 -9 Silicate

Volcanic Ash --- --- -13

Halloysite 5.16 10.1 -13

Vermiculite 5.34 28.9 -15

Cionnabar 4.14 9.49 -16

Organic Materials

Testosterone 14.73 11.01 -2

Chloresterol 14.0 37.8 -2

Metaldehyde --- --- -5

�-Napthol 8.09 17.8 -8.5

Phloroglucinol --- --- -9.4

BacteriumPseudomonas Syringae

--- --- -2.6Bacteria in Leafmold

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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.

Appendix: Sample Questions

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 everydayexperience?

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?

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Lecture 10: Precipitation and Charge Generation

1. The Initiation of Warm Rain

Much of the World’s precipitation occursin the tropics from clouds at temperaturegreater than 0(C. The process initiatingthis warm rain then involves only liquidwater.

The figure to the right show the spreadin the sizes of cloud droplets. There is acontinuous spectrum of droplet sizesfound within any cloud.

Larger heavier droplets fall at greaterspeeds than the smaller lighter ones. Arain drop is a large cloud droplet that islarge enough to fall to the ground beforeevaporating into the unsaturated air belowthe cloud. The smaller cloud droplets fallmore slowly and would evaporate beforefalling very far below the cloud base.

In forming raindrops, cloud droplets must increase in volume by more than a factor of 1000. Itis known that rain can develop within 20 minutes of cloud formation. Condensation can not explainthis 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 growand 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 brokenlines above. The larger drops grow at the expense of the smaller ones. If there is an updraft (as ina cloud), the large drops will take longer to fall through the cloud and the growth process isextended. This is demonstrated in the following “quantitative model” of the production of a largerain drop within a warm cumulus cloud.

The drop leaves thebase of the cloud with aradius of 2.5 mm. Thisprocess is enhanced whenthe drop grows larger andbreaks apart as theirsurface tension iso v ercome by t h efrictional forces of thepassing air and/orcollisions. The fragmentsthen rise again in theupdraft and grow again torepeat this process; achain reaction. This leadto heavy rainfall. Thesteps in the process are asfollows:

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 aslightly higher fall velocity than the average. These larger drop mightcollide with smaller drops lying in its fall path and coalescence mayoccur. Consider a drop of radius r1 (we shall call the collector drop)which is overtaking a smaller droplet of radius r2. As the collector dropapproaches the droplet, it will tend to follow the air streamlines aroundthe collector drop and might miss collision (and coalescence). We candefine an effective collision cross-section r* (shown in the figure to theright) which represents the critical distance between the centre line ofthe collector drop (fall direction of the centre of the collector drop) andthe centre of the droplet such that all droplets within the distance willcollide with the collector drop. Conversely, any droplet outside thisdistance will not collide. Therefore, the effective cross-section of thecollector drop is then %r*2, whereas the geometrical collision cross-section is %(r1 + r2)

2. We can therefore define the “CollisionEfficiency” (e) as:

Lecture 10, Page -3-

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(a) A stream of water droplets of about 100 µmrebounding from a layer of water. (b) At anincreased angle, droplets coalesce.

Determining the value of collision efficiency is an extremely difficult mathematical problem. Theresults of one computerised model is shown below; showing the collision efficiency as a functionof 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 thestreamlines around the collector drop. A the ratio increase, the efficiency increases rapidly (dropletsless likely to follow streamlines). Also note that efficiencies can be greater than unity (1) when thedrops are nearly the same size due to wake effects behind the collector drop. It should also be notedthat 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/ordroplet 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.

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2. The Initiation of Cold Rain

If a cloud extends above the 0(C level, it is called a cold cloud. Cold clouds may containsupercooled water droplets and/or ice particles. If a cloud contains both, it is said to be a “mixedcloud”. 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 ambienttemperature and supersaturation. The basic crystal habit is a hexagonal face (six sides). If the axisnormal to the hexagonal face is long, it is called “ prism-like” ; if shortthen “ plate-like” .

The surface to volume ratio if greatest for fernlike dendrites.Dendrites form when the temperature is about -15(C, when the growthrate is greatest. This crystal structure provide ambient vapour moresurface on which to deposit.

2.2. Growth of Ice Crystals

a) Growth by deposition: In a cloud that contains a large fraction ofsupercooled droplets, the air in the cloud will be saturated withrespect to liquid water. However, under these conditions, theair will be supersaturated with respect to ice. (At -10(C, air thatis saturated with respect to liquid water will have asupersaturation of 10% with respect to ice). As a consequence,the ice particles in a mixed cloud will grow at the expense ofthe water particles.

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-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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b) Growth by riming; hailstones: Riming is the process by which supercooled drops freeze whencoming in contact with an ice particle. In the extreme, this process can result in theformation of graupel and hail.

c) Growth by Aggregation: Aggregation is the process by which ice particles collide and clumptogether to form larger particles. The adhesion of colliding ice particles depend on thetemperature. In general, the higher the temperature, the stickier the surfaces. Also, dendritestend to become entwined.

3. Charge Generation (Separation)

All clouds are electrified to some degree. However, in some convective clouds, the electricalcharges that build up are strong enough to give rise to thunderstorms. The average thunderstorm

Lecture 10, Page -7-

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(shown in the figureto the right) containsa net positive charge(� +24 coulombs) inthe upper (glaciated)regions, a net negativec h a r ge (� - 2 0coulombs) in thelower (mixed) regionjus t above thefreezing line, and asmall net charge (�+4 coulombs) belowthe melting level. There are three theories as to the cause of charge separations in clouds. The firsttwo deal with a phenomenon known as the “thermoelectric effect” in ice. In a rod of ice, if thereis a temperature difference from one end to the other, there will be a small charge separation withinthe rod; with the colder end having a slight negative charge. The theories of ice particle developmentare: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 theice crystal is taken upwards in by updraft.

b) Supercooled droplet collides with hail stone. During freezing of droplet, a negatively chargedice 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 particlerebounds with positive charge.

Lecture 10, Page -8-

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? Howmany 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 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 theleader advances about 50 m, with a time of approximately 50 µs between steps. It is believed thatthe stepped leader start by a local discharge in the bottom of the cloud. As the negatively chargedstepped leader approaches the ground, it induce positive charges on the ground (especially protrudingobjects). When the stepped leader is close to the ground(10 - 100 m), a stroke moves up from theground to meet it. A connection is made and a large current produces the lightning stroke. After thefirst stroke of electricity, a number of subsequent strokes can occur; usually within 100 ms of theprevious stroke. Most lightning flashes contain 3 or 4 strokes. A lightning stroke can raise thetemperature of the air inside the channel of the it passes through to above 30,000(C and pressure of100 atmosphere, before the air has time to expand. The channel expands rapidly creating a powerfulshock wave which we hear as thunder.

Lecture 11, Page -2-

2. Cloud Morphology

2.1. Mechanisms for Formation

Clouds form in air which has become supersatured, usually through ascent accompanied by adiabaticexpansion 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 ms-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 velocitiesdepend 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 fogwhen warm moist air moves over a cold surface.

• Adiabatic expansion and cooling due to a rapid local reduction in pressure; responsible forformation of funnel clouds associated with tornadoes.

2.2. Types of Clouds

The international cloud classification system was proposed by Luke Howard in 1803 and basedon Latin names.

Cumulus: A pile or heap. Convective cloudsStratus: A layer. Layer cloudsCirrus: 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 -3-

2.2.1. Convective clouds

• Cumulus, Cumulonimbus

Lecture 11, Page -4-

2.2.2. Layer Clouds

• Cirrus, Altostratus, Nimbostratus, Altocumulus, Stratocumulus, Cirrocumulus

Lecture 11, Page -5-

2.2.3. Orographic Cloud

Orographic lifting can result in varoius different cloud types over various heights. Their formationis due to lifting of air over a surface feature such as a mountain. The motion of the air results inknown as a mountain wave, and can be produced. On the lee-side of the mountain, the clouds willevaporate in down-ward moving air, resulting in regions of low seasonal rainfall known as rainshadows. Sometimes, on the lee-side the mountain will induce and vertical oscillation known as leewaves, 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 overcontinental regions during the summer. The following is an idealised three stage model of the lifecycle of an air-mass thunderstorm. In the first stage, known as the “Cumulus stage”, the cloudconsists entirely of a warm buoyant plume of uprising air, with air being entrained into the cloudfrom the sides and bottom. Air at the top of the cloud has updrafts on the order of 10 m s-1. Becauseof this large updraft, supercooled liquid cloud droplets exist above the freezing line, which is pulledupwards with the updraft. The second stage, known as the “Mature stage”, is characterised by theformation of a strong downdraft coinciding with the region of greatest rainfall. The downdraft isformed by frictional drag on the air from the falling raindrops and is cooled by evaporative coolingof raindrops below the cloud base. Supercooled droplets exists above the freezing line in the updraftregion, and below the freezing line in the downdraft. Maximum updrafts are in the middle of thecloud, and maximum updrafts are found near the bottom of the cloud. As precipitation develops

Lecture 11, Page -6-

throughout the cloud, the downward motion takes over the cloud. This is the third stage, known asthe “Dissipation stage”. Deprived of theupdraft of supersatured air, clouddroplets no longer grow andprecipitation soon ceases.

In general, only about 20% of thewater vapour that condenses in a cloudreaches the ground in precipitation. Theremainder either evaporates or breaks upinto smaller clouds (such as cirrus). Air-mass thunder storms are generally shortlived and sometime produce destructivewinds and hail.

3.1. Hail

Hailstones is precipitation in the form ofhard pellets or lumps of ice. Generallyhail stones have diameters of between 1and 5 cm. Under extreme conditions,

Lecture 11, Page -7-

they can be larger. The largest recorded hailstone fell in Kansas in 1970 and was 14 cm in diameterand 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 inclouds which have high liquid water content. Hail begins as a small ice pellet or “graupel” thatgrows by riming of supercooled water droplets. Its surface temperature may rise to 0(C due to therelease of the latent heat of freezing, and some of the collected water may remain unfrozen. If thepellet encounters an updraft, it can be carried aloft only to begin another downward journey. Thismay 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 andlight layers. These layer result from changing conditions in the hailstone formation as it movesthrough the cloud. The dark layers result from trapped air bubbles which correspond to rapidfreezing of coalesced water droplets. The clear section is where there is no trapped air andcorrespond to when the hailstone was growing wet.

Lecture 11, Page -8-

3.2. Multi-Cellular Thunderstorms

A multi-cellular thunderstorms is a large thunderstorm system comprised of a number of individualstorm-cells at different stages of development. These tend to be the most severe form ofthunderstorm and form under conditions of veering winds with height. In cases of severe multi-cellular storms it is observed that the individual storm cell will move along the mid-troposphericwind direction while low-level windows come in from the right. Because the low-level inflowcomes in from the right, the storm-cells originate in the right and dissipate to the left. Continuousgeneration of new cells on the right propagates the multi-cellular thunderstorm.

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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’sLaw’s of motion can only be applied if the acceleration (rotational acceleration) of coordinate frameis 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 airinclude pressure gradient forces, gravityand friction (exerted by neighbouringparcels of air of a surface).

1.1.1. Pressure Gradient Force

Consider the horizontal pressure gradientforce on a parcel of air with a height dzand a width of dn (where n is ahorizontal direction with a pressuregradient, and s is the horizontal directionperpendicular to n). By the same logicused in Lecture 1 to derive thehydrostatic equation, we can derive the ahorizontal pressure gradient force. Assuming that the pressure gradient over the distance dn issmall, then we can approximate that the horizontal change in pressure is:

But pressure is defined as the force per unit area, therefore, the horizontal force on the parcel is:

where the negative sign indicates that the force is directed in the opposite direction to the directionof increasing pressure. If we divide by the mass of the air in the parcel (' dn ds dz), where ' is thedensity of the air, we obtain the pressure gradient force per unit mass:

Similarly, the vertical pressure gradient force is:

Lecture 12, Page -2-

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ρ

It is important to note that the force is proportional to the gradient of the pressure field, not to thepressure field itself.

1.1.2. Gravity

newton’s law of gravitation states that the force of gravitybetween on an object of mass m due to an object of mass M,separated by a distance r is equal to:

where G is the universal gravitation constant (G = 6.673 × 10-11 N m2 kg-2 ). The force per unitmass (the gravitational acceleration) on the atmosphere by the gravitational attraction of the Earthis:

where g* = 9.81 m s-2 at sea level.

1.1.3. Friction

Throughout most of the atmosphere, frictional forces are sufficiently small and can, to first orderbe neglected. A notable exception is the planetary boundary layer corresponding to roughly thelowest 1 km of the atmosphere where frictional drag forces due to the surface and turbulence can belarge.

1.2. Apparent Forces Acting in a RotatingCoordinate System

Consider an object being rotated about acentral point. In order for the object toremain in circular motion there must be aninwards directed force called the centrifugalforce. For example consider a ball on astring. In order to maintain circular motion,the string pulls the ball inwards. Theacceleration of the ball towards the centre is

Lecture 12, Page -3-

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The Earth rotates with a period of one day. Therefore it has an angular velocity 7 of:

Now consider an object that is travelling on the Earth’s surface with a zonal (east-west) velocity ofu (a north-south velocity is called a meridional velocity). The zonal velocity u is defined aspositive if the relative motion is in the same sense as the Earth’s rotation (u > 0, westerly flow); andnegative if opposite (u > 0, easterly flow). Therefore, to an observer outside the Earth’s rotationframe, an object travelling on the surface of the Earth with a zonal velocity of u will have a totalvelocity of (7R + u). Because the parcel is travelling in circular motion, it has an accelerationtowards the centre of the Earth of:

From the viewpoint of someone standing on the Earth, the centripetal acceleration is only u2/R (thereal force) and yet there are two more terms. This apparent violation of Newton’s laws can beeliminated by introducing apparent forces per unit mass of 7

2R (a static term) and 27u (a linearterm), directed away from the axis of rotation.

1.2.1 Gravity

A mass on the surface of the planet will experiencea gravitation force mg* directed towards the centre ofthe planet. However, due to the rotational motion ofthe planet, a component of the gravitational force isused to supply the centrifugal force. Therefore, invector form:

The gravitational force is directed towards the centreof the Earth whereas the centrifugal force is directedaway from the axis of rotation. Therefore, except atthe poles and the equator, gravity is not directedtowards the centre of the planet. The Earth, however, has adjusted to this effect as the equatorialradius is 21 km larger than polar radius. As a result, the local vertical does not pass through thecentre of the planet; except at the poles and the equator.

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Lecture 12, Page -4-

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1.2.2. The Coriolis Force

The second apparent force is the Coriolis force andis fundamentally different from the 7

2R term in that

Lecture 12, Page -5-

it is dependent of the zonal velocityu. It is directed outwards from theaxis of rotation in a westerly motion,and inward in an easterly motion.For westerly motion, the horizontalcomponent of the Coriolis forcepushes the object equator-ward. TheCoriolis force also arises for motionsmoving radially towards or awayfrom the axis of rotation. This is dueto the principle of conservation ofangular momentum. In a meridionalm o t i on , t h e conserva t i on o f momen tum induces a zona l mo t i o ndue to the Coriolis force. In the northern hemisphere, the Coriolis Force results in motions beingdeflected to the right (and deflected to the left in the Southern hemisphere). Consider a region of lowpressure in the Earth’s atmosphere. If the Earth was not rotating, the winds would blow inwardstowards the low. But in a rotating atmosphere, the winds are deflected to the right setting up acounter-clockwise flow (clockwise in the Northern-hemisphere).

Lecture 12, Page -6-

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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 thisperson 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 equalledthe force of gravity at the equator?

Lecture 12, Page -7-

3) It is a common belief that in the Northern hemisphere when you pull a plug in a drain, the waterwill flow to create a counter-clockwise vortex over the drain. (And clockwise in the Southernhemisphere). This effect is attributed to the Coriolis force. Can you estimate how large this forceis 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 howmuch is the apparent force of gravity on this person changed when the car is travelling eastwardcompared to westward? Compare this to the same person standing on the pole.

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Lecture 13: Atmospheric Dynamics II

1. Geostrophic Winds

Under conditions where there are no frictional forces or other forces arising from thermal effectsand curvature of flow, the motions of air are a product of the Coriolis force and the pressure gradientforces. A flow of air under a condition of balance between these forces, is known as a geostrophicwind. Such winds, which form in the layer of the atmosphere above the boundary layer (aboveapproximately 1 km), the tends to be smooth and locally uniform.

Consider a parcel of air that is initially at rest in a pressure field as shown in the figure to theright. The parcel will begin to move towards the lower pressure. As the velocity of the parcelincreases, 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 pressuregradient wind and the Coriolis force. At this point the winds will blow the parcel parallel with theisobars as the geostrophic winds.

The geostrophic balance is only valid for situations where the Coriolis force is large. Near theequator, where the Coriolis term is small there is no geostrophic balance. Also, friction andcurvature in the isobars provide important steering mechanisms.

Friction is an important forceform motions within the boundarylayer; where frictional drag of thesurface affects motion. Friction actsin the opposite direction of motion,tending to decrease the speed thusdecreasing the Coriolis force. A newbalance between forces is created,where the pressure gradient force isbalanced by the vector sum of thefrictional and Coriolis forces. Undersuch a balance, the parcel of air driftsslowly towards the lower pressure region. In general, as one increases height above the surface, thefrictional drag decreases and the angle between the winds and the isobars decreases.

Under conditions of curvature in isobars, another steering force comes into play: centripetalforce. Under conditions of curved isobars (ie: circular motion), a component of the inward directedforce must provide the centripetal force for the parcel to follow the isobars. For a low pressure cell,

Lecture 13, Page -2-

the pressure gradient force provides the centripetal acceleration and the Coriolis force balance whatis left. For a high pressure cell, the opposite occurs. As a result, the wind velocities around a lowpressure centre are lower (known as subgeostophic flow or cyclonic flow) than around a highpressure 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 theequator), the airflow in the middle and upper troposphere is westerly. The reason for this is shownin 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. Thisresults in a horizontal pressure gradient aloft. Under a condition of geostrophic flow, the winds will

Lecture 13, Page -3-

blow from the west. (The same logic can be used in the southern hemisphere to explain the westerlyflow).

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 lowpressure centre is known asconvergence. An example is airflow into the centre of a cyclone.Divergence occurs when there isan outflow of air from a region ofhigher pressure, such as from ananticyclone. In general, if air isconverging at the surface, then theair must be rising and diverging atthe top of the troposphere.Similarly, if air is converging atthe top of the troposphere, then airmust be sinking and diverging atthe surface.

3. Scales of Motion in theAtmosphere

All circulations are caused by regional temperature differences which arise from un even heating ofthe earth’s surface by the Sun. The scales of this circulation is highly variable but is organised intopatterns of varying sizes and life-spans. The scales of these motion are summarised in the followingtable:

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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 tominutes

< 1 km Turbulence, dust devilsand gusts

Lecture 13, Page -4-

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3.1. Mesoscale Circulation

Mesoscale winds or local winds are small scalewinds which are generated by local uneven heatingof the Earth. One example of such a wind is theland-sea breezes. Such breezes are created bytemperature differences between the land a seasurfaces at different times of day. In the morningunder calm conditions, there is little temperaturedifference between the land and sea surfacesresulting in no pressure gradient between the landand sea surfaces. As the day proceeds, the land heatquicker than the sea resulting in a horizontal pressuregradient between the land and sea. (The sea does notheat as fast as land because of different water has ahigher albedo and the heat that is absorbed can betransported away by currents). This results in acirculation pattern where are rises over land anddescends over the sea. This circulation ischaracterised by a breeze coming inland from thesea; sea-breeze. At night, the land cools by radiativecooling and the sea cools very slowly (due to currentsin the water transporting heat). The results in areversal of the circulation pattern and winds blowingout to sea; land-breeze.

3.2. Macroscale Circulation

One of the first attempts to explain global circulationpatterns was made by George Hadley in 1735. Hadleyproposed that the large temperature variation between thepoles and the tropics would produce a circulation pattern,

shown to the left,that was similar tot h e l a n d - s e abreezes. In thes t rong heatedtropical regions,the air would risea n d m o v ep 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 -5-

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In the 1920's, a three cellhemispherical model ofatmospheric circulation wasproposed to fit observed data.The figure to the right showsthis model along with thesurface winds. The first cellis locates in the zone betweenapproximately 0( and 30(latitudeand if often called theHadley Cell. Because of theCoriolis force, winds tend tobe easterly. In the middlecell, surface flows tends to bepoleward and the Coriolisforce results in a generalwesterly flow.

Lecture 13, Page -6-

Lecture 13, Page -7-

Appendix: Sample Questions

1) How might have Macroscale circulations effected the first European explorer who discoveredNorth America?

2) Calculate the geostrophic winds at a level of 70 kPa at a latitude of 60( with isobars at rightangles to meridians and a horizontal pressure gradient of 0.1 kPa per ( latitude.

Lecture 14: Atmospheric Dynamic III

1. Jet streams

Embedded in the westerly flow of themid-latitudes, is high speed streamsof wind known as Jet Streams. Thesestreams, which occur just below thetropopause, are narrow (�1 to 2 km)and wide (100 to 500 km). Windspeeds at the centre of the jet aretypically 125 km h-1, but can reach upto 500 km h-1. The source of thesejets is the temperature contrasts onthe surface producing pressuregradients aloft. During winter periods thehorizontal temperature variation on theEarth’s surface may be very large over asmall distance. This results in large pressuregradients aloft and strong geostrophic flow.

In the mid-latitudes, large temperaturegradients are often associated with the polarfront. The frontal region is associated withthe convergence of the cold polar easterliesand the warmer westerlies. The jet thatresults is known as the polar jet stream. Thisstream varies seasonally, moving furthersouth and becoming stronger during thewinter season (due to greater temperaturegradients in the winter caused the expansionand strengthening of the polar vortex). It alsovaries over shorter time scales with wavespushing 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 thecirculation of surface storms and also directs their paths of movement (mid-latitude low pressurecyclones often follow the jet stream). Consequently, observation of the jet stream is an importantcomponent of modern forecasting.

2. Atmosphere - Ocean Interaction

The atmosphere and ocean do not act as separate systems, but can influence each other. Oceanscover 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

Lecture 14, Page -2-

system. Also, friction between the winds and the ocean surface provides a drag force which tendsto drive the ocean circulation. In equatorial regions, the ocean currents tend to be easterlycorresponding to the easterly trade winds. In the mid-latitudes, the currents tend to be westerly. Likethe atmosphere, the circulation of the oceans are also effected by the Coriolis force, resulting incircular current patterns which are found in every major ocean basin. In the north Atlantic, a portionof the equatorial current is deflected north by the prevailing westerlies. The stream, known as theGulf 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, colderwater. This effect is most known on eastern coasts, such as California. The equator-ward motionof the ocean tends to draw water up to replace water the has moved.

3. Air Masses

Regional weather patterns are oftenstrongly influenced by the motions of largebodies of air called Air Masses. Air massesare large bodies of air which arecharacterised by source regions andhomogeneous physical properties, such ashumidity and temperature. When these airmasses move out of it region of origin, theyeffect the weather in other regions.

Lecture 14, Page -3-

Air masses are classified by there source regions, depending on the latitude and nature of thesource region. Classification and identification is by a two letter code making reference to thelatitude {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 weatherproducing systems is the mid-latitude cyclone.These cyclones are large low pressure regionswhich travel eastward and last for periods of daysto weeks. They are characterised by a counter-clockwise circulation. They most often haveassociated with them both a cold and a warm fronta extending from a central area of low pressure.Forced frontal lifting of air results in clouddevelopment and precipitation. The circulationoften results in a comma shaped cloud pattern.

3.1. Fronts

Fronts are boundaries between separate contrasting air masses and are usually characterised by rapidchanges in temperature and humidity. On weather maps they are represented by lines showing theinterface at the surface (except in the case of occluded fronts). Above ground, the front slopes at anangle with warmer less dense air rising over the cooler more dense air.

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3.1.1 Warm Fronts

A warm front occurs when warmerair displaces cooler air. As the coolerair retreats, friction with the groundgreatly slows the motion at thesurface. Consequently, the warmfront forms a shallow wedge with anangle of approximately 0.25( to 0.5(.As the warm air pushed over the frontslowly rises, it expands and coolsoften forming clouds and sometimesprecipitation, even in stableconditions. Due to the slow rate ofascent, the cloud form are usuallymiddle to high levels clouds, such asnimbostratus, 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 iswedged 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, whichgreatly enhances its buoyancy and precipitation intensity. Sometimes cold fronts can result in violentweather 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 frontsspeeds. 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

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cyclone.d) The difference in speeds of fronts results in the occlusion of the fronts and the lifting of the

warm air mass.

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3.3. Cyclogenesis

Upper airflow is important in thedevelopment of cyclonic andanticyclonic motion. Early in thehistory of upper-a i r f lowmeasurements, it was discovered thatthe position of mid-latitude pressuresystems were often dependent on theposition and meanderings of the polarjet. It was noticed that where a“ridge” results in anticyclonic motionand a trough results in a cyclonicmotion. Such surface activities tendto be stronger during the winter when

the polar jet tend to wander northand south more. It was also noticedthat in regions of upper airconvergence and divergence alsoinduced cyclonic (and anti-cyclonic)motions. Consequently, surfacecyclones (and anticyclones) tend toform directly under the jet, andfollow the motions of the jet.

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Appendix: Sample Questions

1) Although the formation of the occluded front represents the period of maximum intensity ofcyclone, 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 15: Atmospheric Optics

Acknowledgements: Image/Text/Data from the University of Illinois WW2010 Project.http://ww2010.atmos.uiuc.edu/

1. Atmospheric OpticsAtmospheric 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 andice crystals. The optical interactions that occur include refraction, reflection, scattering, anddiffraction.

1.1. Optics of Atmospheric Liquid WaterDroplets

One of the most commonly observedatmospheric optical phenomena is therainbow. Rainbows result from refraction-reflection-refraction process of Sun lightpassing through water droplets. Light thatenters the droplet is refracted. However, theangle of refraction is dependent on thewavelength of the light. Blue light isrefracted (bent) more than Red light. Thelight passes through the droplet till it hit theback of the droplet, where some of the light isreflected. If the angle of incidence is greater the 48(, then all the light is reflected. The light thatleaves the droplet emerges at angles between 40((blue or short wavelength) and 42( (Red or longwavelength) of the incoming beam. If enough

Lecture 15, Page -2-

droplets are in the sky, then theintensity of this refracted light isenough to see a rainbow.

1.1.1. Secondary Rainbows

On very rare occasions, asecondary rainbow can be observed.They occur due to a two reflectionprocess. Instead of one rainbow, twoare seen; the second at a larger angle from the anti-solar point. The due to increased reflection losses,the secondary rainbow is not as intense as theprimary. Also, the colour scheme of the secondarybow 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 shapesare six sided columns and plates. (Both crystals are essentially thesame shape, with the columns having a longer third axis). Theinteraction of Sunlight with these crystal produce a wealth of opticaleffects 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 onwhich surfaces od the crystals the light passes through. Iflight passes through twoof the hexigonal surfaceof a crystal (bottomr i g h t ) , t h e n t h eminimum deflection willbe 22(. It light passesthrough one of thehexagonal faces and outon of the perpendical

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faces, the minimum deflection is 46(. Each of these deflections canresult in an atmospheric optical effect.

The refraction of lightthrough two faces of thehexagonal crystal results intwo possible opticalphenomena. The first is a22( halo around the Sun.This is a result fromrandomly oriented icecrystals 22( away from theSun refracting light towardsyou, the observer. Thesecond effects results fromthe non-random orientationof plate ice crystals. Fallingplate crystals in still air tendto fall with a perpendicularface down. This results inbright spots to the left andright of the Sun at 22(,called Sun Dogs.

The refraction of lightthrough one of the

hexagonal faces and one of the perpendicular faces results in asimilar 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 insome interesting optical effects known as pillars. Pillarsresult from single reflections off the surfaces of crystals.Consider, for example, single reflection off the

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perpendicular surface of plate crystals when the Sun in lowto the horizon. If the wind conditions at low, then thesecrystal will fall generally oriented with the largest face down.Reflection off of the perpendicular surfaces results in pillarsof light extending above and below the Sun.

1.3. Atmospheric Refraction

The Earth’s atmosphere is not of constantdensity, of varies with height (pressure) and airtemperature. As such, light travelling through thedoes not travel in s straight line, but is refracted as itmoves into regions of changing density. This resultsin 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 airclosest to the lake is often cooler than the air above.As a result a temperature inversion can occur causingthe light rays to be bent downwards. The apparent image of the boat is elevated, and in known asa superior mirage. Sometimes this effects allow one to see things that either over the horizon orblocked by other object. (Note is effect is sometime not so noticeable. This is because, not only theboat 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 oftenoccur in deserts when the air at the surface is very hot, but cools rapidly with height. This resultsin increased refraction as light passes closer to the ground. This can result in the inversion of anobject in the distance. Such mirages can sometime be seen on highways, where an image of a carin the distance appears below the car.

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O h O O

O O M O M2

2 3

+ → ++ + → +

ν

O O O

O h O O3 2

3 2

2+ →+ → +ν

Lecture 16: The Stratosphere

1. Structure of the Stratosphere

The Stratosphere is a region of theatmosphere which extends fromapproximately 10 to 50 km altitude and ischaracterised by region of increasingtemperature with height. This gradientstrongly inhibits vertical motions and istherefore very stable (or stratified). Sincethere is very little vertical mixing, it remainsclose to radiative equilibrium. It radiativebudget is dependent on the absorption ofincoming solar radiation (primarily in theUV), and the emission of infrared radiation(primarily by CO2). The thermal structure isdetermined by the distribution of ozone (O3).Due to the variation in latitudinal heating andthe geostrophic balance, the majority of themotion of the stratosphere is zonal (east-west), with only a small meridionalcomponent to transfer heat.

1.1. Ozone Photochemistry

The first treatment of stratospheric O3

chemistry was by Chapman in 1930. Heconsidered the formation of Ozone by thephotolysis of oxygen into atomic oxygen followed by a three-body reaction to form ozone:

The photolysis of ozone requires UV radiation of wavelengths of 242 nm or shorter. Ozone couldthe be destroyed by reaction with atomic oxygen or by photolysis by UV radiation 310 nm or shorter.

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The plot to the right shows thetheoretical Chapman profile and theobserved tropical and extra-tropicalconcentrations. O3 productionpeaks in the mid-stratosphere near30 km, below which decreases dueto the extinction of UV in the solarbeam above.

1.2. Involvement of Other Species

Other atmospheric species tend todisrupt the destruction processes ofstratospheric ozone. The classicprocess is the chemical catalyticdestruction cycle:

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R O R O O

R O O R O

+ → ++ → +

3 2

2

R O O R O+ + → +3 22

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 chemicalmakeup 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 columnwould assume, in thousandths of a centimetre, if it was brought to standard temperature and pressure.ie. 400 DU = 4 mm).

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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 amajor role in the destruction of O3 in the stratosphere. It was thought that most of the Cl was lockedup in one of the two Cl reservoir species (HCl and ClONO2). However, upon the discovery of theO3 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 plungedinto darkness, the stratosphere begins to cool. A circulation known as the polar vortex begins toextend up above the level of the tropopause (due to the cooling) and prevents the mixing ofstratospheric air between the inside and outside of the vortex. Also, the temperatures drop lowenough for ice clouds to form in the polar stratosphere (Polar Stratospheric Clouds, PSCs). On theseclouds, HCl and ClONO2 condense, and in the heterogeneous phase they react, releasing largeamounts of gaseous Cl2. Over the winter, the Cl2 builds up in the stratosphere. In the spring, whenthe Sun returns to the polar region, the Cl2 is quickly split into atomic Cl and begins to catalyticallydestroy O3. Due to the amount of Cl in the stratosphere, O3 is almost completely destroyed beforethe 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 Experimenthttp://auc.dfd.dlr.de/GOME/