Transcript Atmospheric Spectroscopy

Atmospheric Spectroscopy
A look at Absorption and Emission
Spectra of Greenhouse Gases
Our Atmosphere
Diagram taken from http://csep10.phys.utk/astr161/lect/earth/atmosphere.html
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
Earth’s Radiation Budget
Electromagnetic Spectrum
Near Infrared
Thermal Infrared
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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)
Electromagnetic Spectrum
Near Infrared
Thermal Infrared
Diagram modified from www.spitzer.caltech.edu/Media/guides/ir.shtml
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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)
Blackbody Radiation Curves for Solar and
Terrestrial Temperatures
Diagram taken from Peixoto and Oort (1992)
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Without greenhouse gases the temperature of the Earth’s 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
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
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
h2
m a2
2
• Electronic energy α
• Vibrational energy α
a
• Rotational energy α
2
=> visible/ultraviolet
=> thermal/near infrared
mM
2
Ma 2
=> 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
electronic
rotational
vibrational
Energy level diagram of CO2 molecules showing relative energy
spacing of electronic, vibrational, and rotational energy levels
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(v+1/2) and v = (1/2π)(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
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)
Harmonic Oscillator Approximation for
Polyatomic Molecules
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Evib = G(v1,v2,…) = ∑ vj(vj’+1/2)
where vj’= 0,1,2,… are the vibrational quantum numbers
vj = (1/2π)(k/µ)1/2 is the frequency of vibration
and k is the bond force constant
Selection rules: Δvj = ±1
This means that in the motion of a polyatomic molecule = motion of Nvib
harmonic oscillators, each with their own fundamental frequency vj =>
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 doesn’t 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.
Rotational Transitions of Polyatomic
Molecules
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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 π2 c IA) B = h / (8 π2 c IB)
where by convention IA > IB > IC
C = h / (8 π2 c IC)
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If IA = 0, IB = IC
If IA = IB = IC
If IA = IB ≠ IC
If IA ≠ IB ≠ IC
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Due to the selection rule ΔJ = 0, ±1, the rotational band is divided into P (ΔJ = -1), Q
(ΔJ =0), and R (ΔJ = +1) branches
A pure rotational transition (Δv=0) can only occur if molecule has permanent dipole
moment
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linear (CO2)
spherical top (CH4)
symmetric top
asymmetric top (H20, O3, N20)
Linear Molecules
• Ia = 0, Ib = Ic.
Erot = BJ(J+1)
• Centrifugal Distortion Correction for polyatomic
molecules (less rigid than diatomic molecules)
= -D[J(J+1)]2 + higher terms
Spherical Tops
• IA = IB = IC
• Quantum mechanics can solve the energy of a spherical
top exactly
• Result: Erot(J,K) = F(J,K) = BJ(J+1) J = 0,1,2…
degeneracy: gJ = (2J+1)2
• Selection rule: ΔJ = 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: -D[J(J+1)]2
Symmetric tops
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Quantum mechanics can also solve symmetric tops
Ia = Ib < Ic
=> oblate symmetric top (pancake shaped)
Ia < Ib = Ic
=> prolate symmetric top (cigar shaped)
Oblate sym top:
Erot(J,K) = F(J,K) = [BJ(J+1) + (C-B)K2]
degeneracy: gJK = 2J+1 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(J+1) + (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:
ΔJ = 0 ,±1 ΔK = 0 for K ≠ 0
ΔJ = ±1 ΔK = 0 for K = 0
Where ΔJ = +1 corresponds to absorption and ΔJ = -1 to emission
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.
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
Earth’s energy budget, effectively increasing temperature of Earth’s
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
√(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 inertiadivides molecules into four catagories (linear, spherical top,
symmetric top, assymetric top). Each has own energy eigenvalues
and selection rules.
Rovibrational Energy
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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, ΔJ = 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)
The Primary Greenhouse
Gases
H 20
• Most important IR absorber
• Asymmetric top → Nonlinear, triatomic molecule has complex line
structure, no simple pattern
• 3 Vibrational fundamental modes
o
H
o
H
symmetric stretch
v1 = 2.74 μm
bend
v2 = 6.25 μm
asymmetric stretch
v3 = 2.66 μm
• Higher order vibrational transitions (Δv >1) 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
Absorption Spectrum of H2O
v1=2.74 μm
v3=2.66 μm
v2=6.25 μm
CO2
• Linear → no permanent dipole moment, no pure rotational spectrum
• Fundamental modes:
o
c
o
symmetric stretch
v1 = 7.5 μm => IR inactive
asymmetric stretch
v3 = 4.3 μm
bend
v2 = 15 μm
bend v2
• v3 vibration is a parallel band (dipole moment oscillates parallel to
symmetric axis), transition ΔJ = 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
IR Absorption Spectrum of CO2
v3
Diagram modified from Peixoto and Oort (1992)
v2
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
o
o
o
symmetric stretch
v1 = 9.01 μm
o
bend
v2 = 14.3 μm
asymmetric stretch
v3 = 9.6 μm
– 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
IR Absorption Spectrum of O3
v1/v3
Diagram taken from Peixoto and Oort (1992)
v2
CH4
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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 => No pure rotational spectrum
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Fundamental modes
H
C
C
H
C
C
H
H
v1
v2
v3 = 3.3 µm
v4 = 7.7 µm
IR Absorption Spectrum of CH4
v3
Diagram taken from Peixoto and Oort (1992)
v4
N2 O
• Linear, asymmetric molecule (has permanent dipole moment)
• Has rotational spectrum and 3 fundamentals
• Absorption band at 7.8 μm broadens and strengthens methane’s 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
bend
v2 = 17.0 μm
IR Absorption Spectrum of N2O
v3=4.5 µm
v1=7.8 µm
v2=17 µm
Diagram taken from Peixoto and Oort (1992)
Total IR Absorption Spectrum for the
Atmosphere
V
i
s
i
b
l
e
Diagram taken from Peixoto and Oort (1992)
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. 915.
• 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.