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 • 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

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/Media/guides/ir.shtml

Blackbody Radiation Curves for Solar and Terrestrial Temperatures • 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 Diagram taken from Peixoto and Oort (1992)

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 • Electronic energy α => visible/ultraviolet • Vibrational energy α => thermal/near infrared • Rotational energy α => 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 • 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 kis 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 • 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) C = h / (8 π2 c IC) where by convention IA > IB > IC • If IA = 0, IB = IC => linear (CO2) • If IA = IB = IC => spherical top (CH4) • If IA = IB ≠ IC => symmetric top • If IA ≠ IB ≠ IC => asymmetric top (H20, O3, N20) • 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

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 • 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 inertia- divides molecules into four catagories (linear, spherical top, symmetric top, assymetric top). Each has own energy eigenvalues and selection rules.

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, 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

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 (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 o o H H bend v2 = 6.25 μm symmetric stretch v1 = 2.74 μm asymmetric stretch v3 = 2.66 μm

Absorption Spectrum of H2O v1=2.74 μm v2=6.25 μm v3=2.66 μm

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 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 o c o symmetric stretch v1 = 7.5 μm => IR inactive asymmetric stretch v3 = 4.3 μm bend v2 = 15 μm bend v2

IR Absorption Spectrum of CO2 v3 v2 Diagram modified from Peixoto and Oort (1992)

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

IR Absorption Spectrum of O3 v1/v3 v2 Diagram taken from Peixoto and Oort (1992)

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 => No pure rotational spectrum • Fundamental modes H C C C C H H H v4 = 7.7 µm v3 = 3.3 µm v2 v1

IR Absorption Spectrum of CH4 v3 v4 Diagram taken from Peixoto and Oort (1992)

N2O • 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 = 17.0 μm bend v2

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. 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.

Atmospheric Spectroscopy