The Earth’s neutral atmosphere
Joachim Vogt
Course 210131, Fall 2010
General Earth and Space Sciences
Course unit on
Space and Atmospheric Physics
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Course 210131, Fall 2010
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Overview
Part I: Physical principles of atmosphere formation
Gravity vs. temperature, escape velocity vs. thermal velocity
Planetary atmospheres in the solar system
Earth’s overall radiation balance
Part II: Composition and vertical structure
Troposphere, stratosphere, mesosphere, thermosphere
Barometric law, atmospheric scale height
Part III: Atmospheric wind and global circulation
Pressure gradient and Coriolis force
Three-cell convection pattern
Appendix
Review questions and further reading
Additional problems and sample solutions
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The Earth’s neutral atmosphere – Part I
Physical principles of
atmosphere formation
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What is an atmosphere ?
An atmosphere is the gaseous envelope around a celestial body.
Planets and some large satellites have atmospheres, asteroids don’t. Why ?
Important factors controlling the state of an atmosphere are
gravity – attracts atmospheric particles,
temperature – controls how fast particles move (away ?) on average,
composition – lighter particles tend to move faster than heavier ones.
To overcome the planet’s gravitational attraction, the kinetic energy must
be larger than the gravitational potential energy. Escape velocity :
p
Vesc =
2GM/r .
G: gravitational constant, M : planetary mass, r: planetocentric distance.
Exosphere: outer region of an atmosphere where collisions are so rare that
sufficiently fast particles can escape into space.
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Temperature, particle mass, and average speed
Characteristic (average, most probable) velocities of a particle population
are determined by the temperature T and by the mass m of a particle.
The thermal (most probable) velocity can be written as
p
Vth =
2kT /m .
To sustain an atmosphere, the thermal velocity should be considerably
smaller than the escape velocity :
2
Vth2 Vesc
⇔
kT GM m/r .
Planets and large satellites (large M ) can have atmospheres whereas
small bodies (asteroids or comets) cannot.
Colder atmospheres (small T ) are more stable.
Heavy constituents (large m) are easier to keep than lighter ones.
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Planetary atmospheres in the solar system (1)
Venus
Earth
Mars
Jupiter
Temperature (◦ C)
465
−89 . . . 58
−82 . . . 0
−150
Gravity (Earth=1)
0.9
1
0.4
2.6
Escape velocity
10.4
11.2
5.0
60
Composition
CO2
N2 & O 2
CO2
H2 & He
Mean surface temperature, gravity at the equator, escape velocity in km/s, and
main atmospheric constituents. Numerical values are taken from table (1).
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Exercise: Thermal vs. escape velocity
Sample question: Compute the thermal velocities of nitrogen molecules
near the Earth’s surface assuming an average temperature of T ≈ 290 K.
You may use of the ’handy’ formula derived in the appendix
s
Vth
T /[K]
= 128.9
[m/s]
Mmol /[g]
where Mmol is the mass of one mol (here measured in grams).
Answer : For N2 , Mmol /[g] ≈ 28 and
s
r
Vth
T /[K]
290
= 128.9
= 128.9 ·
= 128.9 · 3.22 = 414.8 .
[m/s]
Mmol /[g]
28
As expected, this is much smaller than Vesc = 11.2 km/s.
Question A: Repeat this exercise for helium and molecular hydrogen
in the Jovian atmosphere.
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Planetary atmospheres in the solar system (2)
[Voyager 1/NASA (2)]
Jupiter
Joachim Vogt (Jacobs University Bremen)
[Pioneer Venus/NASA (2)]
Venus
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Planetary atmospheres in the solar system (3)
[Hubble/NASA (5)]
Mars
Joachim Vogt (Jacobs University Bremen)
[Cassini/NASA (2)]
Titan
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Earth’s overall radiation balance
Temperatures and emissions
Solar surface, T ≈ 5800 K
⇒ thermal radiation mostly in the visible range: ’shortwave radiation’.
Earth’s surface, T ≈ 300 K
⇒ thermal radiation mostly in the infrared: ’longwave radiation’.
The Earth
receives and absorbs shortwave radiation from the Sun, and
emits longwave radiation into space.
Radiation equilibrium: absorption equals emission.
Important for the interpretation of Earth observations from space (e.g.,
weather satellite images):
infrared images provide information on the temperature distribution,
visible radiation is reflected sunlight: surface reflectivity.
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Earth’s overall radiation balance (continued)
[PhysicalGeography.net (3)]
Shortwave radiation cascade
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Longwave radiation cascade
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Absorption in the atmosphere
[NASA (4)]
The atmosphere absorbs harmful high-energy radiation (UV, x-rays, gamma rays).
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The Earth’s neutral atmosphere – Part II
Composition and
vertical structure
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Composition of the Earth’s atmosphere
Average volume percentages in
the Earth’s dry atmosphere:
N2
O2
Ar
CO2
78.08%
20.95%
0.903%
0.036%
Values taken from (3).
Water vapor: variable
contribution, usually 0–4%.
[GOES/NASA (6)]
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Atmospheric layers
The temperature profile defines
transition zones = ’. . . pauses’
(temp. minima or maxima)
and
layers = ’. . . spheres’
(in between the pauses).
Tropopause at ∼ 11 km:
temp. minimum ∼ −55◦ C;
Stratopause at ∼ 50 km:
temp. maximum ∼ 0◦ C;
Mesopause at ∼ 90 km:
temp. minimum ∼ −90◦ C.
[NOAA/Jetstream (7)]
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Troposphere
The troposphere is the region between the surface and the tropopause.
It contains 80% of the total mass of the Earth’s atmosphere.
Thinner at the poles (∼ 8 km) than at the equator ∼ 18 km.
Water in all phases, weather phenomena.
Temperature decreases with height at a rate of
∼ 6.5◦ C/km = environmental lapse rate.
Troposphere and tropopause form the lower atmosphere.
Greenhouse effect leads to a temperature increase of about 30–40◦ C.
Visible light (shortwave) penetrates the atmosphere, heats the surface.
Resulting thermal radiation is in the infrared (longwave) range.
Longwave radiation is partially absorbed and re-emitted by
greenhouse gases like CH4 , CO2 , water vapor . . .
⇒ higher surface temperature.
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Greenhouse effect illustrated
[PhysicalGeography.net (3)]
Enhanced greenhouse effect: human activities add greenhouse gases which
lead to further increase of the tropospheric temperature.
⇒ global warming.
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Stratosphere and mesosphere
Stratosphere
Region between tropopause and stratopause containing about 20% of
the total mass.
Mass of the troposphere and stratosphere taken together:
∼ 99.9% of the total mass of the atmosphere.
Close to the tropopause:
isothermal layer (constant temperature), about 9 km thick.
Temperature increase with height:
associated with the presence of ozone in the stratosphere.
Mesosphere
Region between stratopause and mesopause.
Temperature decrease with height.
Stratosphere and mesosphere together form the middle atmosphere.
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Ozone layer in the middle atmosphere
The middle atmosphere protects the biosphere from a broad wavelength
range of harmful UV radiation through the formation of ozone (O3 ).
Absorption of UV radiation by molecular oxygen (O2 ) in the ranges
175 nm < λ < 200 nm (mesosphere) and
200 nm < λ < 242 nm (stratosphere)
leads to dissociation of O2 .
Combination of O and O2 yields ozone (O3 ).
Ozone: further UV absorption for 200 nm < λ < 340 nm.
UV absorption gives rise to the temperature maximum at the
stratopause (unique feature of Earth’s atmosphere).
Ozone depleting substances (such as chlorofluorcarbons CFCs) are
stable in the troposphere but degrade under the influence of UV light
in the stratosphere.
Montreal Protocol (1987): agreement to stop production of CFCs
until 1996/2010 in more/less developed countries.
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Thermosphere, heterosphere, ionosphere
Thermosphere
Neutral atmosphere above the mesopause.
Characterized by an increase of temperature with height.
Absorption of hard UV radiation (λ < 175 nm).
Also called upper atmosphere.
Structure criteria other than temperature: composition and ionization.
Heterosphere (above ∼90–100 km): atmospheric constituents are no
longer mixed by turbulence – composition is changing with height.
The lower and the middle atmosphere (homogeneous mixture of
atmospheric gases) form the homosphere.
Ionosphere (above ∼ 70 km): ionized component of the upper atmosphere
– characterized by significant conductivities and electrical currents.
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Exercise: Ionization potentials
Sample question: The ionization potentials (= energies required to ionize
neutral particles) of the most abundant gases in the Earth’s atmosphere
are in the range of 15 eV. Show that green light (λ = 550 nm) does not
contribute to the formation of the Earth’s ionosphere.
Note that 1 J = 6.24 · 1018 eV.
Answer : The energy of green light
hc
6.626 · 10−34 Js · 2.998 · 108 m/s
E =
=
λ
0.55 · 10−6 m
= 3.6 · 10−19 · 6.24 · 1018 eV = 2.2 eV .
This is too small to overcome the ionization thresholds.
Question B: Which kind of radiation is required to ionize the Earth’s
(upper) atmosphere ?
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Air pressure
Pressure is force per area. SI unit: Pascal (= 0.01 mbar = 10−5 bar).
Gravity g causes pressure to decrease with
height z. In isothermal regions the pressure
profile follows the barometric law :
p(z) = p0 e−z/H .
The atmospheric scale height
H =
kT
mg
is a measure of atmospheric ’thickness’.
Close to the surface: H ≈ 8.3 km.
[PhysicalGeography.net (3)]
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The Earth’s neutral atmosphere – Part III
Atmospheric wind and
global circulation
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Pressure gradient force (PGF)
Wind is air in motion. Motion is initiated by forces. Most important for
global wind systems and circulation patterns are the
pressure gradient force (pressure difference per distance) which drives
wind from high to low pressure, and the
Coriolis force: due to the rotation of the Earth, moving objects (incl.
gases) are deflected from straight paths.
Pressure gradient force (PGF)
Isobars (e.g. on weather maps): lines of
constant pressure.
Direction of PGF: perpendicular to isobars.
Strength of PGF: indicated through the
density of isobars.
[PhysicalGeography.net (3)]
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Sea breeze
[Images from the University of Illinois WW2010 Project (8)]
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Coriolis force (CF)
The Coriolis force (CF)
deflects air in motion
to the right of its path
on the Northern
hemisphere, and
to the left of its path
on the Southern
hemisphere.
Strength of CF depends on
wind speed v and
geographic latitude β.
[PhysicalGeography.net (3)]
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Geostrophic wind
Circulation patterns characterized by
a balance of PGF and CF are called
geostrophic.
Geostrophic winds flow along
isobars.
This is a good approximation for
large-scale convection pattern.
[PhysicalGeography.net (3)]
Northern hemisphere
High-pressure centers are associated with clockwise rotation.
Low-pressure centers go along with anti-clockwise rotation.
Southern hemisphere: high p.c. ↔ anti-clockwise, low p.c. ↔ clockwise.
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Measured average temperature distribution
Average Annual Global Temperature 1982-1994
[PhysicalGeography.net (3)]
Temperature Scale in Kelvin
Measured variation is approximately latitudinal (combined effect of solar
radiation and Earth’s rotation). Non-latitudinal variations are due to
differences in the heat capacities of land and ocean, altitude, albedo.
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Model global circulation pattern (1): CF disregarded
Without the Coriolis force, i.e.,
if only the pressure gradient force
was active, then on each hemisphere
we would have one large convection
cell (cf. sea breeze model):
flow near the tropopause from
the equator (= region of high
pressure) to the poles (= region
of low pressure),
surface return flow from the
poles to the equator.
[NOAA/Jetstream (7)]
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Measured global circulation pattern – January
[PhysicalGeography.net (3)]
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Model global circulation pattern (2): CF considered
Coriolis force deflects the convection
and leads to additional zones of
(horizontal) convergence and
divergence.
Three cell model of global
circulation:
(1) Hadley cell
(2) Ferrel cell
(3) polar cell.
[NOAA/Jetstream (7)]
Hadley cell (latitudes of about 0◦ –30◦ ):
air rises at equator, upper air moves poleward,
CF deflects to the right, air sinks at ∼ 30◦ ,
equatorward surface return flow, deflection by CF yields
northeasterly and southeasterly trade winds.
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Three cell model of global circulation
Hadley cell (continued):
belt of high surface pressure at ∼ 30◦ : subtropical ridge,
low pressure near the equator: near equatorial trough,
horizontal inflow of wind near the equator: intertropical convergence zone.
Polar cell (latitudes of about 50/60◦ –90◦ )
cold, dense air descends at the pole, causing high surface pressure,
equatorward flow near the surface, deflection to the right due to CF yields
surface polar easterlies,
upper air return flow to the pole completes convection cell.
Polar vortex: upper tropospheric portion of the polar convection.
Ferrel cell (latitudes of about 30◦ –50/60◦ ):
convection cell in between the Hadley cell and the polar cell.
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Jet streams
[NOAA/Jetstream (7)]
Jet streams are
wind systems in the upper troposphere and lower stratosphere,
concentrated in narrow bands,
flowing from west to east at boundaries of hot and cold air masses.
Subtropical jet stream: latitude β ∼ 30◦ .
Polar jet stream: latitude β ∼ 60◦
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The Earth’s neutral atmosphere – Part IV
Appendix
Joachim Vogt (Jacobs University Bremen)
The Earth’s neutral atmosphere
Figures and references
(1) Values taken from the Windows to the Universe web page
http://www.windows.ucar.edu/tour/our solar system/planets table.html
at the University Corporation for Atmospheric Research (UCAR).
(2) NASA’s Solar System Exploration website http://solarsystem.nasa.gov/.
(3) Figure taken from the educational web portal PhysicalGeography.net
http://www.physicalgeography.net/fundamentals/7i.html created by
Michael Pidwirny, University of British Columbia Okanagan.
(4) Figure taken from NASA’s Imagine the Universe web site
http://imagine.gsfc.nasa.gov/docs/science/know l1/emspectrum.html.
(5) Image taken from Hubblesite http://hubblesite.org/ – a gallery of images
taken by the Hubble Space Telescope operated by NASA.
(6) NASA’s Earth Observatory web page http://earthobservatory.nasa.gov/.
(7) Information and images taken from the Online Weather School Jetstream
http://www.srh.noaa.gov/jetstream/ at NOAA.
(8) Images taken from the University of Illinois WW2010 Project, see
http://ww2010.atmos.uiuc.edu/.
All URLs were checked on September 23rd, 2005.
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Review questions and further reading
Review questions
What are the key factors that control the state of an atmosphere, and how
can you quantify the processes in terms of characteristic velocities ?
Which planets or large satellites in our solar system sustain an atmosphere ?
Which spectral ranges contribute most to the thermal radiation spectra of
the Sun and of the Earth ? Describe briefly the processes associated with the
Earth’s global radiant energy balance.
Characterize the composition of the Earth’s atmosphere.
Sketch the temperature profile in the Earth’s atmosphere, and name the
boundary layers associated with temperature maxima and minima.
Characterize the troposphere and explain the greenhouse effect.
Discuss the role of ozone in the middle atmosphere.
Define the terms thermosphere, heterosphere, and ionosphere.
What are the barometric law and the atmospheric scale height?
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Review questions and further reading (continued)
Review questions (continued)
What is meant by the pressure gradient force, and how does it relate to an
isobaric chart? Characterize the processes that lead to sea breeze.
Explain how the Coriolis force affects air in motion, and characterize
geostrophic wind.
Based on the observed average annual temperature distribution on the
Earth’s surface, what kind of global circulation pattern would you expect if
our planet was non-rotating?
Describe the basic pattern of the measured global circulation, and
characterize the phenomena associated with the main convection cells.
Textbooks
R.A. Freedman, W.J. Kaufmann: Universe.
M. Kivelson, C.T. Russell: Introduction to space physics.
J.K. Hargreaves: The solar-terrestrial environment.
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Review questions and further reading (continued)
Web resources
The textbook by Freedman and Kaufmann comes with a web page:
http://bcs.whfreeman.com/universe6e/.
HyperPhysics web page hosted by the Department of Physics and
Astronomy at Georgia State University:
http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html.
Educational web portal PhysicalGeography.net created by Michael Pidwirny,
University of British Columbia Okanagan:
http://www.physicalgeography.net/ (chapters 6 and 7).
http://www.srh.noaa.gov/jetstream/: NOAA’s Online Weather School
Jetstream.
The interpretation of weather-satellite images is explained in an Introductory
Meteorology Lab Exercise at http://funnel.sfsu.edu/satlab/ created
by Dave Dempsey, Dept. of Geosciences, San Francisco State University.
The series of European weather satellites Meteosat was built by the
consortium EUMETSAT , see http://www.eumetsat.int/.
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Additional questions and problems
Problem 1
Dissociation of molecular oxygen (in the mesosphere and the stratosphere)
requires UV radiation with wavelengths smaller than 200 nm. What is the
corresponding energy (in eV) ?
Problem 2
The thermal
p (most probable) velocity of a (maxwellian) particle population
is Vth =
and the average velocity is given by
p 2kT /m, p
Vav = 3kT /m = 3/2 Vth . Here T is the temperature of the gas, and
m is the mass of a single particle. To work out characteristic velocities for
different gases and temperatures, it is more convenient to use the mass
Mmol of one mol instead of m, and to absorb the constants into a single
numerial value. Show that
s
s
Vth
T /[K]
Vav
T /[K]
= 128.9
and
= 157.9
.
[m/s]
Mmol /[g]
[m/s]
Mmol /[g]
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Sample solutions of the problems
Sample solution of problem 1
The energy E = hc/λ of UV radiation at wavelengths λ = 200 nm is given by
6.626 · 10−34 Js · 2.998 · 108 m/s
E =
= 9.9 · 10−19 · 6.24 · 1018 eV = 6.2 · eV .
1
−6
0.2 · 0 m
Sample solution of problem 2
In SI units, the formula for the thermal (most probable) velocity is written as
s
−1
T
m
Vth
k
=
.
2
[m/s]
[J/K] [K] [kg]
The mass Mmol of one mol of a substance is the mass of NA = 6.0221 · 1023
particles (Avogadro’s number). We obtain
m
Mmol 1
Mmol [g] 1
Mmol
1
=
=
=
.
[kg]
[kg] NA
[g] [kg] NA
[g] 1000 NA
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Sample solutions of the problems (continued)
Sample solution of problem 2 (continued)
This gives
Vth
[m/s]
s
k
T
2
1000 NA
[J/K]
[K]
=
√
=
Using Vav =
p
Mmol
[g]
−1
s
2 1.38 · 10−23 · 1000 · 6.0221 · 10−23
s
=
128.9
3kT /m =
T
[K]
p
Mmol
[g]
Mmol
[g]
−1
−1
.
3/2 Vth yields
Vav
Vav
= 1.225
= 157.9
[m/s]
[m/s]
Joachim Vogt (Jacobs University Bremen)
T
[K]
s
T
[K]
The Earth’s neutral atmosphere
Mmol
[g]
−1
.
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