Interaction of matter and radiationsatellite.mpic.de/pdf_dateien/interaction.pdf · Interaction...

Interaction of matter and radiation

Basic effects:

-Scattering(molecules/particles)

-Absorption (molecules/particles)

-Emission (molecules/particles/surfaces)

-Refraction

-Reflection

Interaction of matter and radiation

-Absorption (molecules)

-electronic transitions

-vibrational, rotational transitions

-Absorption (particles)

-Scattering

-Rayleigh, Raman-scattering

-Particle (Mie-) scattering

-Thermal emissison

-Refraction

-Reflection

http://rst.gsfc.nasa.gov/Intro/Part2_1a.html

Knowledge on interaction of matter and radiation is necessary for the interpretation of remote sensing results

( ) ( ) ( ) ( ) ( ) ( ) ( , )s a adI I I B T

dsλ ε λ λ ε λ λ ε λ λ= − ⋅ − ⋅ + ⋅

Streuung Absorption Thermische Emission

Radiative transfer equation:

Remote sensing through analysis of electromagnetic radiation(absorption or emission)

Electromagnetic radiation in the atmosphere

UV/Vis and near IR: Electronic and vibrational transisons (typ. Absorption)

Thermal IR: Vibrational transisons (typ. Emission)

Microwaves: Rotational transisons (typ. Emission)

The electromagnetic spectrum

Troposphärische DOAS-Messungen

- Langpfad-Anordnung:

SpiegelLichtquelle& Spektrograph

0.5 - 15 km

Effects: Absorption, scattering

Active methods: Continuous light sources in the UV/vis

Tropospheric Longpath DOAS observations

Light source Mirrorand spectrometer

⎭⎬⎫

⎩⎨⎧

⋅⎟⎠

⎞⎜⎝

⎛+−⋅= ∫ ∑

l

si

ii dssII0

0 )()()(exp)()( λερλσλλ

Beer- Lambert-law :

σi: Absorption cross section of trace gas iρi: Concentration of trace gas iεs: Scatter coefficient

=> From the knowledge of the absorption cross section it is possible todetermine the trace gas concentration

Absorption spectroscopy

Effects: Absorption, scattering

http://pcl.physics.uwo.ca/pclhtml/introlidar/introlidarf.html

LIDAR Light detection and ranging

Active methods: Pulsed light sources in the UV/vis

Effects: Absorption, scattering, reflection, refraction

Passive DOAS observations (scattered or direct light)

Passive methods: UV/vis Absorption spectroscopy using extraterrestrial light sources

Effects: Absorption, scattering, refraction

Passive methods: UV/vis Absorption spectroscopy using extraterrestrial light sources

Passive DOAS observations (direct light)

Effects: Emission, scattering, absorption

Passive methods: IR/microwave emission spectroscopy

Thermal emission

Atmospheric remote sensing from theCRISTA instrument (IR)

Mechanisms discussed today:





-Scattering



-Thermal emissison

-Refraction

-Reflection





Absorption/Emission spectra of molecules show characteristic structures => molecules can be identified and quantified by these ‘fingerprints’

What determines these spectra?

-position (wavelength) of absorption/emission line: difference of energy levels of the transition

-strength of absorption/emission line: probability of the transition

Example of trace gas cross section:

H2O absorption cross section for 290K

(HITRAN data base)

How can spectra be determined?

(depending on properties of the molecules)

UV/Vis and near IR: Electronic and vibrational transisons (typ. Absorption)

Thermal IR: Vibrational transisons (typ. Emission)

Microwaves: Rotational transisons (typ. Emission)

Usually a combination of the different transition types occur

Different types of transitions:

Electronic transitions:

Energy levels:

-transitions between different energy levels of an atom (quantum mechanic)

-wavelength depends on energy differences

ΔE = E2 – E1 = hν, λ * ν = c

-rough estimation of the energy levels:

-diameter of molecules ~a few 10 nm

-from uncertainty relation: Δp ~ / a => Ee ~ Δp/2me

(me: mass of electron)

=> Wavelength is in the visible and UV spectral range


Energy levels:

-exact energy levels can be determined using (time independent) Schrödinger equation,

Example: Hydrogen atom

-energy levels are of the order of electron volts

Example: Hydrogen atom: -Lyman series: ≤ 13.6 eV (≥ 95 nm)

-Balmer series: ≤ 3.4 eV (≥ 430nm)

-Paschen series: ≤ 1.5 eV (≥ 1282nm)


Transition probability:

-atomic interaction with radiation can be described as an atomic system which is disturbed by a (small) time-dependent disturbance

-time dependent Schrödinger equation

-the Hamiltonian of the undisturbed system be H0

-it describes the energy levels and the time evolution of the undisturbed system:

-then the Hamiltonian of the total system can be described by H(t) = H0 + H1(t)




-For wavelengths larger than the size of the atom

the dipol approximation is sufficient:

-Transition probability:

-Matrix element must be ≠ 0 => selection rules for dipole radiation:

Considering polarisation and non-coherent light:

Bnm = Bnm : Einsteincoefficients for absorptionand induced emission

Vibrational transitions:

Energy levels:

-for small amplitudes Hooks law can be applied: V(r) = mω²r²/2

(m: atomic mass, k = ω²: force)

The force originates for the valence electrons; the order of magnitude can thus be estimated by V(a) ≈ mω²a² ≈ Ee

=> Wavelength is in the IR

Rotational transitions:

Energy levels:

-transition between different states of Rotational Energy

with ma² the inertia moment

=> Wavelength is in the far IR and microwave region

Molecular motions

Translation: Translation: Motion ofMotion of the complete moleculethe complete molecule inin three three dimensionsdimensions..

Rotation: Rotation: Rotation ofRotation of the complete molecule around three the complete molecule around three axesaxes..

Vibration: Vibration: periodic motionperiodic motion ofof individual atomsindividual atoms relative relative toto each othereach other..

AA molecular with two atomsmolecular with two atoms hashas the following degreesthe following degrees ofoffreedomfreedom::::

TranslationTranslation: 3: 3

Rotation: 2Rotation: 2

Vibration: 1Vibration: 1

In three dimensions

Around the twolateral axes

Degrees of freedomThe individual atomsThe individual atoms of aof a molecule can movemolecule can move inin three three dimensionsdimensions.. The combined motionThe combined motion of allof all atoms can be atoms can be described as Translationdescribed as Translation, Rotation and, Rotation and vibrationvibration ofof the the moleculemolecule..AA molecule withmolecule with N N atomsatoms has 3N has 3N degreesdegrees ofof freedomfreedom..

Degrees of freedom

Geneal rule for degreesGeneal rule for degrees ofof freedom for vibrational motion freedom for vibrational motion forfor aa molecule withmolecule with NN atomsatoms::

For linearFor linear moleculesmolecules::DegreesDegrees ofof freedom for vibrational motionfreedom for vibrational motion = 3N= 3N--55

For nonFor non--linearlinear moleculesmolecules::DegreesDegrees ofof freedom for vibrational motionfreedom for vibrational motion = 3N= 3N--66

Molecular vibrations

Molecuoles vibrateMolecuoles vibrate,, since the atoms are not fixed but are elasticallysince the atoms are not fixed but are elasticallyboundbound ((like with mechanical springslike with mechanical springs). ).

As in As in the mechanicsthe mechanics,, Hooks law can be appliedHooks law can be applied::

F = F = --k*xk*x

Different kinds of molecular vibrationsExampleExample: CO: CO22 ((DegreeDegree ofof freedom for vibrationfreedom for vibration: 4): 4)

SymmetricSymmetric vibrationvibration Assymmetric vibrationAssymmetric vibration

Deforming vibrationDeforming vibration

Harmonic oscillator

PotentialPotential energy as energy as functionfunction ofof the the displacementdisplacement ::

212

V kx=

Energy levels for different statesof vibration

Energy levelsEnergy levels: : Harmonic oscillatorHarmonic oscillator::

01( )2

⎛ ⎞= +⎜ ⎟⎝ ⎠

E v h vν

v = Schwingungsquantenzahl (v = 0,1,2...)

0

1 2

12

1 1 1Reduzierte Masse:

=

= +

k

m m

νπ μ

μ

Quantum number of vibration

Reduced mass:


TheThe distancedistance between the between the energy levels is constantenergy levels is constant::

ωh

In reality: The anharmonic oscillator

DissociationDissociation ofof the moleculethe molecule

Strong increaseStrong increase of potentialof potentialenergy energy for short distancesfor short distances

In reality: The anharmonic oscillator

MorseMorse--Potential:Potential:

( )21= − a x

eV hcD e

0

2reduzierte Masse2

==

= ⋅

==

e

e

x AuslenkungD Dissoziationsenergie

ahcDμ ω

μω πν

Displacement

Energy for dissociation

Reduced mass


Energy levelsEnergy levels: :

AnharmonicAnharmonic oscillatoroscillator::

2

0 01 1( )2 2

⎛ ⎞ ⎛ ⎞= + − +⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠

eG v v v xν ν

20

2 4= =

he

e

axDν

μω

( ) =E v hν ( )G v


TheThe distancedistance between the energy between the energy levels are not constantlevels are not constant. For. Forincreasingincreasing vv thethe distancedistance decreasesdecreases..There exist onlyThere exist only aa limited numberlimited numberofof eneryg levelseneryg levels..

2

0 01 1( )2 2

⎛ ⎞ ⎛ ⎞= + − +⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠

eG v v v xν ν

Vibrational spectroscopy

The combinationThe combination ofof the possible transitions determines the the possible transitions determines the absorption spectrumabsorption spectrum. .

Molecules absorb electromagnetic radiationMolecules absorb electromagnetic radiation inin thethe IRIR

Transition betweenTransition between differentdifferent statesstates ofof vibrationvibration

Selection rules:InteractionInteraction between the moleculebetween the molecule andand radiation is only radiation is only possible if the electric dipole momentpossible if the electric dipole moment ofof the molecule the molecule changes withchanges with time. Suchtime. Such vibrations arevibrations are IRIR--activeactive..

δ +

Selection rules:

AnAn oscillating electric oscillating electric dipole exists if thedipole exists if thepositive and negative positive and negative partialpartial charges movecharges moverelative torelative to each othereach other..

δ − δ −

δ +

δ +

δ +

Selection rules:

δ −δ −

δ +

δ +

rl

rl

DipoleDipole momentmoment

No DipoleNo Dipole momentmoment

DipoleDipole momentmoment

Oscillating dipolOscillating dipol!!

Selection rules:

IRIR--inaktivinaktiv IRIR--aktivaktiv

IRIR--aktivaktiv IRIR--aktivaktiv

SymmetricSymmetric vibrationvibration Assymmetric vibrationAssymmetric vibration

Deforming vibrationDeforming vibration

Specific selection rules:Not allNot all transitions betweentransitions between differentdifferent energy levels are possibleenergy levels are possible::

ForFor the harmonic oscillatorthe harmonic oscillator: :

1vΔ = ±

ForFor the anharmonic oscillatorthe anharmonic oscillator: :

1,2,3,...vΔ = ±HereHere alsoalso transitions over larger distances are possibletransitions over larger distances are possible.. The The probability forprobability for suchsuch transitions decreases with larger transitions decreases with larger differencesdifferences in vin v

Rotational vibrational spectroscopy

WhenWhen aa molecule changes its statemolecule changes its state ofof vibrationvibration,, usually itusually italso aalso a changechange inin the statethe state of rotationof rotation occursoccurs..The reason is that the bounding lengthThe reason is that the bounding length andand thus the inertia thus the inertia moment dependsmoment depends onon the statethe state ofof vibrationvibration..

The rotaional quantum numberThe rotaional quantum number J J changes bychanges by(In(In some casessome cases also also ΔΔJ=0J=0 is possibleis possible))

1±

1vΔ = ± 1JΔ = ±

( )01S(v, J) v BJ J 12

⎛ ⎞= + ν + +⎜ ⎟⎝ ⎠

InIn summarysummary::


Transitions between two neighbouring statesTransitions between two neighbouring states ofof vibrationvibration::

Combined Combined vibrational vibrational rotational rotational transitionstransitions


The corresponding absorption spectrumThe corresponding absorption spectrum::


HereHere also also ΔΔJ=0J=0 is possibleis possible (Q(Q--branchbranch) :) :

IMG spectrum (in transmittance units) in the 600–2500 cm-1 spectral range recorded over South Pacific (-75.24, -28.82) on 4 April 1997, 04:00:42 GMT (top). Radiative transfer simulations for absorption contributions due tostrong (middle) and weak (bottom) absorbers are also provided.

Trace gas measurements from infrared satellite for chemistry and climate applicationsC. Clerbaux1, J. Hadji-Lazaro1, S. Turquety1, G. M´egie1, and P.-F. Coheur2, Atmos. Chem. Phys. Discuss., 3, 2027–2058, 2003

IR absorption spectroscopy in the atmosphere:






-Scattering



-Thermal emissison

-Refraction

-Reflection

Wavelenght dependence of aerosol absorption

as

sKK

K+

=ω~

Single scattering albedo

for different aerosol types(Takemura et al., J. of Climate, 2002)






-Scattering



-Thermal emissison

-Refraction

-Reflection

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0 500 1000 1500 2000 2500

Wavelength [nm]

Sigm

a (re

lative

to ge

ometr

ic cro

ss se

ction

)

Particle radius: 500 nm

Mie extinction cross section (r: 500 nm, refractive index: 1.5)

λ >> r => σ ~ λ-4 (Rayleigh scattering)

λ << r => σ ~ λ-0 (Clouds)

for typical aerosol size distributions: σ ~ λ-1 to λ-1.5

Wavelength dependence of scattering processes

red: s-polarisation, blue: p-polarisation

Angular and polarisation dependence of scattering processes

λ >> r λ < rλ ~ r

1

2

3

4

5

6

7

8

9

10

11

12

0

30

60 90

120

150

210

240 270

300

330

180

Influence of inelastic scattering

300 400 500 600 700 800Wavelength [nm]

0.0

0.2

0.4

0.6

Ref

lect

ivity

320 340 360 380 400Wavelength [nm]

Ref

lect

ivity

‚Filling-in‘ of spectral structures: Ring effect

Comprehensive theory for spherical particles: Mie scattering

( ) ( )22

212

0

8,

RiiIRI

πλ +

=Θ

Mie intensity parameters i1 and i2 (for perpendicular polarised light) are complex functions of the refractive index of the scatterer, the size parameter and scattering angle

λπα r2

=Size parameter:

The (complex) refractive index describes the scattering and absorption properties:

n = nr (1 – ai)

With

nr : real refractive index

a: constant proportional to the absorption coefficient






-Scattering



-Thermal emissison

-Refraction

-Reflection

Thermal radiation:

A black body emits the spectral radiance:

With f: frequency,T: temperature, h the Planck constant, and k the Boltzmann constant

0.0E+00

1.0E-12

2.0E-12

3.0E-12

4.0E-12

5.0E-12

6.0E-12

0 5000 10000 15000 20000 25000 30000 35000 40000

Frequency [GHz]

B(

)d [

W/m

²]

50K100K200K300K

Microwave region, seezoom on next page

For small frequencies the Planck-law can be

approximated by the Rayleigh-Jeans-law

The Rayleigh-Jeans law is a good description for the

microwave region:

0.0E+00

5.0E-15

1.0E-14

1.5E-14

2.0E-14

2.5E-14

3.0E-14

3.5E-14

4.0E-14

0 100 200 300 400 500 600 700 800 900 1000

Frequency [GHz]

B(

)d [W

/m²]

50K100K200K300K

1<<kThν

=> ( ) 2

22c

kTB νν ≈Rayleigh Jeansradiation law

The spectrum of solar radiation outside the Earth’s atmosphere and at sea level (solid lines) compared with black body radiation at 5800 K (dashed line). The atmospheric absorptions are mainly due to O3, O2, H2O and CO2 [Graedel and Crutzen, 1993].

For real emitters, the spectral radiance is smaller than for the ideal black body. The ratio of the actual spectral radiance and that of a black body defines the emissivity. Especially for molecules, the emissivity depends strongly on wavelength. The emitted spectral radiance thus depends on a) the temperature, b) the trace gas concentration, and c) the spectrum of the emissivity. The spectrum of the emissivity is determined by the scheme of the energy levels of the molecule and the respective transition probabilities. The Einstein coefficients for spontaneous emission are related to those for induced emission and absorption.

Einstein coefficients for induced and spontaneous transitions

For a stationary equilibrium of the numbers of atoms in state 1 and 2 we can write:

with the number of atoms in state I, and the spectral radiance.

iN

In thermal equilibrium it follows from the Boltzmann-distribution:

with the statistical weight

kTh

kTEE

egge

gg

NN ν

−−

−==

2

1

2

1

2

112

)12( += Jg

( ) ( )TBNBTBNBNA νν ⋅⋅=⋅⋅+⋅ 112221221

From the combination of these formula it follows:

211

212 B

ggB =

123

3

128 B

chA νπ

=

-for similar statistical weights induced absorption and emission have the same probability.

-the probability for spontaneous emission increases with increasing frequency

Emission spectra measured from stratospheric ballonsoundings at different altitudes

(Bergmann Schaefer, 1997)






-Scattering



-Thermal emissison

-Refraction

-Reflection

Refraction

A rainbow is a prominent example for refraction in the atmosphere. The refraction occurs at the transition from air to water.

Heidelberg, 08.02.2007

Because the concentration of air decreases with altitude also the refractive index of air depends on altitude. Light beams through the atmosphere are subject to continuous refraction. This effect is strongest for slant light paths; thus refraction deforms the shape of the solar disk at sunrise and sunset.






-Scattering



-Thermal emissison

-Refraction

-Reflection

Average surface albedo (610nm) as determined in Koelemeijer et al. [2003].

600 650 700 750 800

620 640 660 680Wavelength [nm]

0.96

1.00

1.04

0.04

0.06

0.08

0.0

0.2

0.4

0.6

0.96

1.00

1.04High pass filtered albedo

Conifers

Decidous

Grass

0.0

0.2

0.4

0.6

0.04

0.06

0.08

Spec

tral A

lbed

o

Spectra of the reflectance over different kinds of vegetation.

Spectral structures after high-pass filtering

© ASTER Spectral Library, courtesy of the Jet Propulsion Laboratory, California Institute of Technology, Pasadena

Surface effects: Bidirectional reflection function BDRF

www.academic.emporia.edu

Sun glint © J.S. Aber

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