Atmospheric Spectroscopy

1
Atmospheric Spectroscopy

• A look at Absorption and Emission Spectra of
  Greenhouse Gases

2
Our Atmosphere
Diagram taken from http//csep10.phys.utk/astr161/
lect/earth/atmosphere.html
3
Composition of the Atmosphere

• N2 78.1
• O2 20.9
• H20 0-2
• Ar other inert gases 0.936
• CO2 370ppm (0.037)
• CH4 1.7 ppm
• N20 0.35 ppm
• O3 10-8
• other trace gases

4
Earths Radiation Budget
5
Electromagnetic Spectrum

• Over 99 of solar radiation is in the UV,
  visible, and near infrared bands
• Over 99 of radiation emitted by Earth and the
  atmosphere is in the thermal IR band (4 -50 µm)

Near Infrared
Thermal Infrared
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Electromagnetic Spectrum

• Over 99 of solar radiation is in the UV,
  visible, and near infrared bands
• Over 99 of radiation emitted by Earth and the
  atmosphere is in the thermal IR band (4 -50 µm)

Near Infrared
Thermal Infrared
Diagram modified from www.spitzer.caltech.edu/Medi
a/guides/ir.shtml
7
Blackbody Radiation Curves for Solar and
Terrestrial Temperatures

• Without greenhouse gases the temperature of the
  Earths surface would be approximately 15 degrees
  Fahrenheit colder than it is today
• This is due to the fact that certain trace gases
  in the atmosphere absorb radiation in the
  infrared spectrum (wavelengths emitted by the
  Earth) and re-emit some of this radiation back
  down to Earth

Diagram taken from Peixoto and Oort (1992)
8
What are the Major Greenhouse Gases?

• N2 78.1
• O2 20.9
• H20 0-2
• Ar other inert gases 0.936
• CO2 370ppm
• CH4 1.7 ppm
• N20 0.35 ppm
• O3 10-8
• other trace gases

9
Molecular Absorption

• The total energy of a molecule can be seen as the
  sum of the kinetic, electronic, vibrational, and
  rotational energies of a molecule
• Electronic energy a gt visible/ultraviolet
• Vibrational energy a gt thermal/near infrared
• Rotational energy a gt microwave/far infrared
• Vibrational transitions (higher energy) are
  usually followed by rotational transitions (lower
  energy) and we thus see groups of lines that
  comprise a vibration-rotation band

10
electronic
rotational
vibrational
Energy level diagram of CO2 molecules showing
relative energy spacing of electronic,
vibrational, and rotational energy levels
11
Vibrational Transitions of a Diatomic Molecule

• The molecular bond can be treated as a spring and
  thus a harmonic oscillator potential can be
  approximated for the molecule
• Evib v(v1/2) and v (1/2p)(k/µ)1/2
• However, polyatomic molecules are more
  complicated due to their more complex structure
• For polyatomic molecules, any allowed vibrational
  motion can be expressed as the superposition of a
  finite amount of vibrational normal modes, each
  which has its own set of energy levels

12
Vibrational Transitions of Polyatomic Molecules

• Any molecule has 3N degrees of freedom, where N
  is the number of atoms in the molecule.
• Translational Degrees of Freedom 3
• Specifies center of mass of the molecule
• Rotational DOF 2 (linear), 3(nonlinear)
• Describes orientation of the molecule about its
  center of mass
• Vibrational DOF 3N-5 (linear), 3N-6 (nonlinear)
• Describes relative positions of the nuclei
• Vibrational DOF represent maximum number of
  vibrational modes of a molecule (due to
  degeneracies and selection rules)

13
Harmonic Oscillator Approximation for Polyatomic
Molecules

• Evib G(v1,v2,) ? vj(vj1/2)
• where vj 0,1,2, are the vibrational quantum
  numbers
• vj (1/2p)(k/µ)1/2 is the frequency of
  vibration
• and k is the bond force constant
• Selection rules ?vj 1
• This means that in the motion of a polyatomic
  molecule motion of Nvib harmonic oscillators,
  each with their own fundamental frequency vj gt
  normal modes
• Vibrational state of triatomic molecule
  represented by (v1v2v3)
• v1 symmetric stretch mode, v2 bending mode,
  v3 asymmetric stretch mode
• Stretching modes of vibration occur at higher
  energy than bending modes
• If dipole moment doesnt change during normal
  mode motion, that normal mode is infrared
  inactive.
• Number of IR active normal modes determines
  number of absorption bands in IR spectrum
• Higher order vibrational transitions lead to
  frequencies slightly displaced from the
  fundamental and of much less intensity due to
  smaller population at higher energy levels.

14
Rotational Transitions of Polyatomic Molecules

• Approximate as rigid network of N atoms (rigid
  rotator approximation)
• Rotation of a rigid body is dependent on its
  principle moments of inertia
• Ixx ? mj (yj-ycm)2 (z-zcm)2
• A set of coordinates can always be found where
  the products of inertia (Ixy, etc) vanish. The
  moments of inertia around these coordinates are
  the principle moments of inertia.
• Spacing between rotational lines described by
  rotational constants
  
• A h / (8 p2 c IA) B h / (8 p2 c IB) C
  h / (8 p2 c IC)
• where by convention IA gt IB gt IC
• If IA 0, IB IC gt linear (CO2)
• If IA IB IC gt spherical top (CH4)
• If IA IB ? IC gt symmetric top
• If IA ? IB ? IC gt asymmetric top (H20, O3,
  N20)
• Due to the selection rule ?J 0, 1, the
  rotational band is divided into P (?J -1), Q
  (?J 0), and R (?J 1) branches
• A pure rotational transition (?v0) can only
  occur if molecule has permanent dipole moment

15
Linear Molecules

• Ia 0, Ib Ic.Erot BJ(J1)
• Centrifugal Distortion Correction for polyatomic
  molecules (less rigid than diatomic molecules)
• -DJ(J1)2 higher terms

16
Spherical Tops

• IA IB IC
• Quantum mechanics can solve the energy of a
  spherical top exactly
• Result Erot(J,K) F(J,K) BJ(J1) J
  0,1,2 degeneracy gJ (2J1)2
• Selection rule ?J 0, 1
• The symmetry of these molecules requires that
  they do not have permanent dipole moments. This
  means they have no pure rotational transitions.
• Centrifugal Distortion Correction -DJ(J1)2

17
Symmetric tops

• Quantum mechanics can also solve symmetric tops
• Ia Ib lt Ic gt oblate symmetric top (pancake
  shaped)
• Ia lt Ib Ic gt prolate symmetric top (cigar
  shaped)
• Oblate sym top
• Erot(J,K) F(J,K) BJ(J1) (C-B)K2
• degeneracy gJK 2J1 J 0,1,2 K
  0,1,2... J where J total rotational angular
  momentum of molecule K component of
  rotational ang. momentum along the symmetry
  axis
• Prolate sym top
• Erot(J,K) F(J,K) BJ(J1) (A-B)K2
• For the sym. top molecules with permanent dipole
  moments, these dipole moments are usually
  directed along the axis of symmetry. The
  following selection rules are assigned for these
  molecules
• ?J 0 ,1 ?K 0 for K ? 0
• ?J 1 ?K 0 for K 0
• Where ?J 1 corresponds to absorption and ?J
  -1 to emission

18
Asymmetric Tops

• IA ? IB ? IC
• Schrodinger eqn has no general solution for
  asymmetric tops
• The complex structure of asymmetric does not
  allow for a simple expression of their energy
  levels. Because of this, the rotational spectra
  of asymmetric tops do not have a well-defined
  pattern.

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Summary of Tuesday

• Atmosphere is composed primarily of N2 and O2
  with concentrations in the ppm of greenhouse
  gases (aside from H20 which varies from 0-2)
• These GHG (H20, CO2, CH4, O3, N20) have huge
  impact on the Earths energy budget, effectively
  increasing temperature of Earths surface by 15
  degrees Fahrenheit.
• GHG absorb largely in the infrared region which
  indicates vibrational and rotational transitions
  of the molecules upon absorption of a photon
• Vibrational energy levels are greater than
  rotational by a factor of v(m/M)
• Vibrational transitions described by fundamental
  (normal) modes which are determined by number of
  vibrational degrees of freedom of that molecule
  3N -5 for linear, 3N-6 for nonlinear.
  Superposition of these normal modes can describe
  any allowed vibrational state.
• Ex) for triatomic molecule, vibrational state
  represented by (v1v2v3) where v1 symmetric
  stretch mode, v2 bending mode, v3 asymmetric
  stretch mode
• Rotational energy levels determined by principle
  moments of inertia- divides molecules into four
  catagories (linear, spherical top, symmetric top,
  assymetric top). Each has own energy eigenvalues
  and selection rules.

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Rovibrational Energy

• Vibrational and rotational transitions usually
  occur simultaneously splitting up vibrational
  absorption lines into a family of closely spaced
  lines
• Rotational energy also dependent on direction of
  oscillation of dipole moment relative to axis of
  symmetry
• When oscillates parallel, ?J 0 transition is
  forbidden and only P and R branches are seen
• When oscillates perpendicular, P, Q and R
  branches are all seen
• The rotational constant is not the same in
  different vibrational states due to a slight
  change in bond-length, and so rotational lines
  are not evenly spaced in a vibrational band

Rovibrational transitions in a CO2 molecule
Diagram taken from Patel (1968)
21
The Primary Greenhouse Gases
22
H20

• Most important IR absorber
• Asymmetric top ? Nonlinear, triatomic molecule
  has complex line structure, no simple pattern
• 3 Vibrational fundamental modes
• Higher order vibrational transitions (?v gt1) give
  weak absorption bands at shorter wavelengths in
  the shortwave bands
• 2H isotope (0.03 in atm) and 18O (0.2) adds new
  (weak) lines to vibrational spectrum
• 3 rotational modes (J1, J2, J3)
• Overtones and combinations of rotational and
  vibrational transitions lead to several more weak
  absorption bands in the NIR

o
o
H
H
bend v2 6.25 µm
symmetric stretch v1 2.74 µm
asymmetric stretch v3 2.66 µm
23
Absorption Spectrum of H2O
v12.74 µm
v26.25 µm
v32.66 µm
24
CO2

• Linear ? no permanent dipole moment, no pure
  rotational spectrum
• Fundamental modes
• v3 vibration is a parallel band (dipole moment
  oscillates parallel to symmetric axis),
  transition ?J 0 is forbidden, no Q branch,
  greater total intensity than v2 fundamental
• v2 vibration is perpendicular band, has P, Q, and
  R branch
• v3 fundamental strongest vibrational band but v2
  fundamental most effective due to matching of
  vibrational frequencies with solar and
  terrestrial Planck emission functions
• 13C isotope (1 of C in atm) and 17/18O isotope
  (0.2) cause a weak splitting of rotational and
  vibrational lines in the CO2 spectrum

o
c
o
symmetric stretch v1 7.5 µm gt IR inactive
asymmetric stretch v3 4.3 µm
bend v2 15 µm
bend v2
25
IR Absorption Spectrum of CO2
v3
v2
Diagram modified from Peixoto and Oort (1992)
26
O3

• Ozone is primarily present in the stratosphere
  aside from anthropogenic ozone pollution which
  exists in the troposphere
• Asymmetric top ? similar absorption spectrum to
  H20 due to similar configuration (nonlinear,
  triatomic)
• Strong rotational spectrum of random spaced lines
• Fundamental vibrational modes
• 14.3 µm band masked by CO2 15 µm band
• Strong v3 band and moderately strong v1 band are
  close in frequency, often seen as one band at 9.6
  µm
• 9.6 µm band sits in middle of 8-12 µm H20 window
  and near peak of terrestrial Planck function
• Strong 4.7 µm band but near edge of Planck
  functions

o
o
o
o
bend v2 14.3 µm
symmetric stretch v1 9.01 µm
asymmetric stretch v3 9.6 µm
27
IR Absorption Spectrum of O3
v1/v3
v2
Diagram taken from Peixoto and Oort (1992)
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CH4

• Spherical top
• 5 atoms, 3(5) 6 9 fundamental modes of
  vibration
• Due to symmetry of molecule, 5 modes are
  degenerate, only v3 and v4 fundamentals are IR
  active
• No permanent dipole moment gt No pure
  rotational spectrum
• Fundamental modes

H
C
C
C
C
H
H
H
v4 7.7 µm
v3 3.3 µm
v2
v1
29
IR Absorption Spectrum of CH4
v3
v4
Diagram taken from Peixoto and Oort (1992)
30
N2O

• Linear, asymmetric molecule (has permanent dipole
  moment)
• Has rotational spectrum and 3 fundamentals
• Absorption band at 7.8 µm broadens and
  strengthens methanes 7.6 µm band.
• 4.5 µm band less significant b/c at edge of
  Planck function.
• Fundamental modes

O
N
N
symmetric stretch v1 7.8 µm
asymmetric stretch v3 4.5 µm
bend v2 17.0 µm
bend v2
31
IR Absorption Spectrum of N2O
v34.5 µm
v17.8 µm
v217 µm
Diagram taken from Peixoto and Oort (1992)
32
Total IR Absorption Spectrum for the Atmosphere
V i s i b l e
Diagram taken from Peixoto and Oort (1992)
33
References

• Bukowinski, Mark. University of California,
  Berkeley. 21 April 2005.
• Lenoble, Jacqueline. Atmospheric Radiative
  Transfer. Hampton, Virginia A. DEEPAK
  Publishing, 1993. 73-91, 286-299.
• McQuarrie, Donald A., and John Simon. Physical
  Chemistry. Sausalito, California University
  Science Books, 1997. 504-527.
• Patel, C.K.N. High Power Carbon Dioxide Lasers.
  Scientific American. 1968. 26-30.
• Peraiah, Annamaneni. An Introduction to Radiative
  Transfer. Cambridge, United Kingdom Cambridge
  University Press, 2002. 9-15.
• Petty, Grant W. A First Course in Atmospheric
  Radiation. Madison, Wisconsin Sundog Publishing,
  2004. 62-66, 168-272.
• Thomas, Gary E., and Knut Stamnes. Radiative
  Transfer in the Atmosphere and Oceans. Cambridge,
  United Kingdom Cambridge University Press, 1999.
  110-120.