Lecture 2: More on the atmosphere

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Lecture 2 More on the atmosphere
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Size and Pressure Variation

• The air provides little resistance to everyday
  activities but is not to be ignored!
• Mass of atmosphere 5.2 x 1018 Kg
• Density 1.2 Kg / m3
• gt99 of atmospheric gases in lower 30 Km altitude
• Gravity leads to a pressure variation with
  altitude
• Can we understand the pressure variation in terms
  of simple models?
• Barometric Distribution Law

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Barometric Distribution Law

• A gas is a fluid and as such obeys the
  hydrostatic equation, which relates fluid
  pressure (P) to height (h) or depth in a fluid
  column. The differential form of the hydrostatic
  equation applied to a fluid is
• dP - r g dh
• For a gas r is the density of the gas and g is
  gravitational acceleration.

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Barometric Distribution Law

• Since gases are compressible, the density of a
  gas will vary with pressure. If we make the
  reasonable assumption that a gas in say the
  atmosphere is ideal, we can write the hydrostatic
  equation as
• dP - ( P M) / (R T) g dh
• Where M is the molar mass

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Barometric Distribution Law

• Solving this differential equation by separating
  variables and integrating
• P1 ? P2 dP / P - h1 ? h2 M g / ( R T )
  dh
• gives, assuming an isothermal atmosphere and
  after rearrangement, the isothermal barometric
  distribution law
• P2 P1 e - M g ( h2 - h1 ) / ( R T )

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Barometric Distribution Law

• According to the isothermal barometric
  distribution law the pressure of a gas in the
  atmosphere should decrease exponentially with
  altitude

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Barometric Distribution Law

• the assumption of an isothermal atmosphere is not
  a particularly good assumption and the
  temperature of the atmosphere actually falls
  linearly with height according to the adiabatic
  lapse rate
• T Tref - Mavg g / Cp, avg ( h - href )

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Why?

• Air pressure decreases with altitude.
• easily understood qualitatively through the
  kinetic molecular theory.
• Random thermal motion tends to move gas molecules
  in all directions equally.
• In the presence of a gravitational field, motions
  in a downward direction are slightly favored.
• This causes the concentration, and thus the
  pressure of a gas to be greater at lower
  elevations and to decrease without limit at
  higher elevations.

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Why?

• Heavier molecules more strongly affected by
  gravity
• their concentrations will fall off more rapidly
  with elevation.
• thus the partial pressures of the various
  components of the atmosphere will tend to vary
  with altitude.
• The difference in pressure is also affected by
  the temperature
• at higher temperatures there is more thermal
  motion, and hence a less rapid fall-off of
  pressure with altitude.
• Because of atmospheric convection and turbulence,
  these effects are not observed in the lower part
  of the atmosphere, but in the uppermost parts of
  the atmosphere the heavier molecules do tend to
  drift downward.

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Why?
Properties of Gases a Chem1 Supplement
Text Stephen K. Lower Simon Fraser University
Decrease of pressure with altitude for air at 25 C
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Consequences of density fluctuations
http//photos.viczhang.com/index.php?showimage657
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Blue Skies!

• Randomness of movement ensures that the molecules
  will quickly distribute themselves throughout the
  volume occupied by the gas in a thoroughly
  uniform manner.
• The chances are virtually zero that sufficiently
  more molecules might momentarily find themselves
  near one side of a container than the other to
  result in an observable temporary density or
  pressure difference.
• This is a result of simple statistics.
• Only valid when the sample population is large.

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Blue Skies!

• What if we had extremely small volumes of space -
  cubes that are about 10-7 cm on each side
• Such a cell would contain only a few molecules
• at any one instant we would expect to find some
  containing more or less than others
• in time they would average out to the same value.
  
• The effect of this statistical behavior is to
  give rise to random fluctuations in the density
  of a gas over distances comparable to the
  dimensions of visible light waves.

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Blue Skies!

• When light passes through a medium with a
  non-uniform density, some light is scattered.
• Scattering due to random density fluctuations is
  called Rayleigh scattering
• shorter wavelengths more effectively scattered
  than longer wavelengths.
• The clear sky appears blue in color because the
  blue (shorter wavelength) component of sunlight
  is scattered more.
• The longer wavelengths remain in the path of the
  sunlight, seen at sunrise or sunset.

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Atmospheric Composition
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Temperature is important!

• Layers of atmosphere are by their temperature
• Troposphere
• Stratosphere
• Mesosphere
• Upper Atmosphere
• Thermosphere
• Exosphere
• Magnetosphere/ionosphere

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http//www.williamsclass.com/EighthScienceWork/Atm
osphere/EarthsAtmosphere.htm
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Troposphere

• first layer closest to the earth
• approx. ground to 10 kilometers
• contains about 75 of the total mass of the
  atmosphere
• where all plants and animals live and breathe
• climate and weather also occur in this layer
• wider at the equator than at the poles
• Temperature and pressure drops as you go higher
  up the troposphere.

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Tropopause

• At the very top of the troposphere is the
  tropopause
• where the temperature reaches a (stable) minimum.
  
• a "cold trap" because this is a point where
  rising water vapour cannot go higher because it
  changes into ice and is trapped.
• If no cold trap, Earth would loose all its water
• The uneven heating of the regions of the
  troposphere by the Sun causes convection currents
  and winds.
• Warm air from Earth's surface rises and cold air
  above it rushes in to replace it.
• When warm air reaches the tropopause, it cannot
  go higher as the air above it (in the
  stratosphere) is warmer and lighter
• prevents much air convection beyond the
  tropopause.
• acts like an invisible barrier and is the reason
  why most clouds form and weather phenomena occur
  within the troposphere.

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Tropopause
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Stratosphere

• approximately 10 km - 45 km above the earth
• Stratosphere troposphere make up 99 of the
  total mass of the atmosphere
• The ozone layer is located here
• stops many of the sun's harmful ultraviolet rays
  from reaching the earth
• The jet stream is located here
• Little or no water vapor here
• The lower portion of the stratosphere
• has a nearly constant temperature with height
• the upper portion of the stratosphere
• the temperature increases with altitude because
  of absorption of sunlight by ozone.
• This temperature increase with altitude is the
  opposite of the situation in the troposphere.

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Stratopause

• temperature drops throughout troposphere until
  the tropopause at 12km,
• then increases throughout the stratosphere until
  the stratopause which peaks at about 50 km.
• This is where most ozone exists and the
  increasing temperatures in the stratosphere are
  due to heating caused by ozone absorbing solar UV
  radiation.
• Above the stratopause the temperature falls again
  in the mesosphere until the mesopause is reached
• then increases up to very large values (1500K)
  in the thermosphere.

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Mesosphere

• Third layer of atmosphere
• approximately 45 km -95 km up
• coldest part of the atmosphere
• temperature can drop to -114 C
• where we see "falling stars,"
• meteors that fall to the earth and burn up in the
  atmosphere.
• At certain times of the year, we can see many of
  these "falling stars" when the earth goes through
  the pieces of a broken comet.
• the atmosphere is very rarefied and the
  temperature generally decreases with increasing
  altitude.

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Mesopause

• temperature drops in both hemispheres up to the
  tropopause but the height of tropopause moves up
  as we go towards the more southern latitudes on
  an August (northern summer) day.
• temperatures at the tropopause get colder as we
  move towards the winter pole reflects the
  effect of less solar heating?
• At the stratopause the temperature gradient is
  not very strong .
• near the mesopause the summer side is colder than
  the winter side!

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http//www.yorku.ca/mcdade/eats4230/Iannotes12.ht
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Thermosphere

• approximately 95 km to 500 km and up
• Warmest layer of the atmosphere, with many temp.
  changes
• can get to 227 C
• Energy from the sun is absorbed and bounced back
  very hot!!!
• few molecules that are present in the
  thermosphere receive extraordinary large amounts
  of energy from the Sun.
• would actually feel very cold to us because of
  the probability that these few molecules will hit
  our skin and transfer enough energy to cause
  appreciable heat is extremely low.

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Ionosphere

• lower layer of thermosphere
• Ionosphere made of electronically charged
  particles.
• reflects radio waves from one location to another
• In the daytime this layer interferes with radio
  waves since suns energy charges the particles too
  much and causes problems a lot of static.
• At night it is less charged.
• This is why it is easier to hear AM radio late at
  night

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Magnetosphere

• Part of the upper atmosphere
• produces the beautiful "northern lights" or
  "aurora borealis."

http//imagery.wordpress.com/category/space/
http//www.allposters.com/-sp/The-Aurora-Borealis-
shimmers-in-the-sky-above-silhouetted-evergreeens-
Posters_i1020187_.htm
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Exosphere

• The exosphere is the highest layer of the
  atmosphere.
• approximantly 500 kilometers and beyond
• The thermosphere and the exosphere together make
  up the upper atmosphere.
• Outer most layer of our atmosphere
• Very very few air molecules in this layer
• No clear boundary between this layer and space

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Function of the Atmosphere

• Protection of all life from hazardous or deadly
  radiation from space (filter for UV- and x-rays
  from sun).
• Letting pass the vitally important sunlight to
  the surface of the continents and oceans (energy
  source).
• Protections from rapid cooling at night and
  heating at day.
• Makes possible a mean temperature on Earth's
  surface of 15 C instead of -18 C as would be
  without atmosphere.

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Function of the Atmosphere

• Transport of energy (warmth of air that can be
  felt and latent warmth of water vapour) from the
  equatorial regions to medium and higher
  latitudes.
• Transport of water vapour through dynamic
  processes of general air circulation that
  determines precipitation.
• Storage of huge amounts of nitrogen (important
  for plants).
• Reservoir for carbon dioxide and oxygen.

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Function of the Atmosphere

• Is part of different vital cycles of matter.
• Dissipation and decomposition (oxidation,
  reaction with radicals, photolysis) of natural
  and anthropogenic (man-made) emissions.
• Protection from smaller meteorites that burn up
  by heating from the friction when entering the
  Earth's atmosphere and can not reach the surface.
  

http//tcal.net/archives/category/events/page/4/
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Radiation and Thermal Structure

• The Earths energy comes from the sun
• The sun behaves (almost) as a source of blackbody
  radiation at 6000 K (almost)
• specific electronic transitions mostly due to
  hydrogen

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A characteristic pattern of spectral lines,
either absorption or emission, produced by the
hydrogen atom. The various series of lines are
named according to the lowest energy level
involved in the transitions that give rise to the
lines.
Consider the Balmer series, in which the four
principal lines, designated as H-a, H-b, H-g, and
H-d, involve energy jumps of 3.02 10-19, 4.07
10-19, 4.57 10-19, and 4.84 10-19 J,
respectively, and corresponding photons of
wavelengths are 656.3, 486.1, 434.0, and 410.2
nm.
http//www.daviddarling.info/encyclopedia/H/hydrog
en_spectrum.html
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Radiation and Thermal Structure

• absorption of light by photosphere of the sun
  causes the intensity in the far ultraviolet to
  fall off more rapidly than for a blackbody at
  6000 K

http//www.warren-wilson.edu/dcollins/WebCamPub/W
ebcam.htm
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The in and out distributions shown in Fig. 1.6
may be approximately with black body radiance
curves for temperatures of about 6000 K (outer
regions of sun) and 250 K (temperature near the
stratopause).
http//www.yorku.ca/mcdade/eats4230/Iannotes12.ht
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A closer look at the spectrum of the incoming
solar radiation shown in Fig 1.7 reveals that a
black body at 6000 K only approximates the
solar in coming spectrum.
At the top of the atmosphere a solar temperature
of  5900 K is really quite good particularly at
the longer wavelengths.  But notice that the
spectrum at the bottom of the atmosphere shows
large gaps were energy has been absorbed by the
atmosphere.   All of these notches in the
spectrum are due to spectroscopic absorption by
minor atmospheric species mostly O3, H2O, and CO2.
http//www.yorku.ca/mcdade/eats4230/Iannotes12.ht
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Fig 1.8 shows the spectrum of the radiance
emerging from the top of the atmosphere, i.e. the
outgoing radiation from Earth and its atmosphere,
as measured with an instrument looking downwards
from the Nimbus 4 satellite.   Here again we see
that a blackbody radiation curve is only a crude
approximation to the outgoing spectrum and there
again appear to be notches cut out of blackbody
radiation curve.  
http//www.yorku.ca/mcdade/eats4230/Iannotes12.ht
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Radiation and Thermal Structure

• At first sight one might think that these
  notches, which occur where CO2, O2 and H2O have
  vibrational absorption bands, simply reflect the
  same absorption phenomena as the outgoing
  radiation.  
• only partly true because in the infrared region,
  absorption of radiation from the ground is not
  the only thing that is going on.
• Absorption plays a big role but re-emission of
  the absorbed or thermal emission radiation by
  these molecules actually fills in the gaps to a
  very significant extent.
• The depths of the notches are not simply related
  to the concentration of the absorbers, as it is
  in the incoming visible case. 
• because of this absorption and re-emission or
  radiative transfer, the strength of the emission
  actually tells us a great deal about the
  temperatures and temperature profiles in the
  atmosphere

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Radiation and Thermal Structure

• temperatures 106 K are characteristic of the
  chromosphere and the corona of the sun.
• Emissions from these regions lead to extreme UV
  and X-ray portions of the solar spectrum.

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Radiation and Thermal Structure

• The temperature of the planet can be estimated by
  balancing the amount of incoming radiation
  absorbed from the sun RA, against the outgoing
  radiation from the Earth, RO.
• Incoming radiation from the sun reaches the
  surface of the Earth, but outgoing thermal
  radiation is re-radiated within the atmosphere
  and not all lost to space.
• Greenhouse Effect
• (higher temperatures than those calculated based
  on radiation balance alone - we did not account
  for an atmosphere)
• Longwave radiation is absorbed by lower parts of
  the atmosphere (lower atmosphere is warmer than
  upper parts)

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http//www.ux1.eiu.edu/cxtdm/met/sirs.html
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Numbers refer to percentage of incoming solar
radiation.
http//soer.justice.tas.gov.au/2003/image/378/inde
x.php