Radiation in the Earth's Atmosphere

Part 1:

Absorption and Emission by Atmospheric Gases

Electromagnetic Waves

● Electromagnetic waves are transversal.

● Electric and magnetic fields are perpendicular.

● In the quantum mechanic context EM waves are travelling photons.

Refraction

Scattering

Absorption

Blackbody Radiation

What is a Black Body?

● An ideal black body absorbs radiation at all frequencies/wavelengts completely.

● A cavity is a good approximation of a black body.

● No real body can absorb more than a black body.

● If a body only absorbs radiation partially, it is called “gray”.

Source: http://web.mit.edu

Blackbody Radiation

● A black body also emits radiation in a characteristic way.

● The emitted radiation only depends on temperature, not on material or other properties.

Source: http://en.wikipedia.org

● The wavelength of the maximum of the radiation is inversely proportional to the absolute temperature:

Wien's Displacement Law

Source: http://en.wikipedia.org

Classical Explanation:Rayleigh-Jeans Law

● For each wavelength/frequency only a certain number of waves fit into the cavity.

Source: http://hyperphysics.phy-astr.gsu.edu

The Ultraviolet Catastrophe

● The classical Rayleigh-Jeans law would produce infinite radiation at short wavelengths.

Source: http://hyperphysics.phy-astr.gsu.edu

● Planck assumed that radiation could only be absorbed or emitted in discrete packets of h=6.626*10-34 J s.

● Planck's law correctly describes the black body radiation between the classical Rayligh-Jeans and Wien approximation.

Planck's Law

Source: http://en.wikipedia.org

Absorption and Emission

Absorption Coefficient

I=I 0 e− l

● The incoming radiation with intensity I

0 is

attenuated by the medium.

● The absorption coefficient α is a measure for the absorption by path length.

● α depends on the wavelength.

● Beer-Lambert-Law:

Kirchhoff's Law for Thermal Radiation

● A blackbody emits radiation with the source term

● The emission coefficient ε ds=1 for a blackbody andε ds<1 for a real body.

● To fulfill the 2nd law of thermodynamics, the emission coefficient ε must be equal to the absorption coefficient α.

S=νB νT

Optical Depth

● We define the optical depth τ as

● Transmission: T = exp(-τ)● τ<<1: optically thin case

● τ>>1: optically thick case

s =∫0

sds' s'

Radiative Transfer Equation

Radiative Transfer

● Electromagnetic radiation traveling through a medium may be absorbed.

● The absorption is proportional to the intensity I. It is characterised by the absorption coefficient α.

● The medium may also emit electromagnetic radiation. This is the source term S.

Radiative Transfer Equation

I ν0 =I ν s0e−s0∫0

s0

ds Bν T e−s

● Intensity at observer's position s=0

● Background radiation at s=s0

● Source (emission) term: B● Units: W/(m2 Hz sterad)

Discrete Radiative Transfer

● The integral form of the radiative transfer equation can be solved numerically.

● Discretize radiative transfer equation into optically thin layers with constant absorption coefficient and convert integral into sum.

● Alternative: calculate radiative transfer iteratively for optically thin layers. Use previous layer as background term.

Molecular Absorption

Atomic and Molecular Spectra● Atoms and molecules may change

between different internal energetic states.

● According to quantum mechanics, only distinct changes are allowed.

● A change from one state to another results in the emission or absorption of a photon of distinct frequency according to Planck's law E=hν.

● There are distinct classes of changes that result in emission/absorption in distinct bands of the electromagnetic spectrum.

Rotational Molecular Spectra

● Molecules rotate around their center of mass

● They emit electromagnetic waves if the charges inside the molecule are not symmetric with respect to the center of mass (permanent dipole moment).

● Typical spectra are in the microwave region.

Vibrational Molecular Spectra

● Molecules vibrate by changing distances between atoms.

● They emit electromagnetic waves if the vibration results in an asymmetric charge distribution (induced dipole moment).

● Typical spectra are in the infrared region.

Vibrational-Rotational Spectra● P branch: ΔJ= -1● Q branch: ΔJ= 0

(often forbidden)● R branch: ΔJ= +1

Pressure (Collision) Broadening● Spectral lines are

broadened by collisions with other molecules.

● A collision interrupts the emission of a continuous elecromagnetic wave. This results in a wider frequency distribution.

● The width of the collision-broadened line is roughly proportional to pressure.

● Pressure-broadening adds altitude information that can be used for profile retrievals.

Effect of Pressure-Broadening Observed at Ground Level

● The observer sees the integral over all emitted lines from all altitudes.

Lorentz- and Doppler Broadening

● Lorentz: natural broadening due to limited lifetime of excited state.

● Doppler: broadening due to the relative thermal speed of the emitting molecules.

Altitude Effect (emission)

Real-World Spectra (absorption)

H2O: 27035 lines CO2: 10757 lines CH4: 7240 lines O2: 1087 lines N2O: 1569 lines CO: 2564 lines +12 additional species

Fine Structure (absorption)

Line-by-line vs. Band Spectra

● Because of the large number of spectral lines, calculationg radiative transfer line-by-line is very costly

● For climate models, average absorption for a larger band is calculated for each species.

● The net absorption is then calculated by scaling the average absorption with temperature and mixing ratio of the trace gases (e.g. CO

2)

Solar and Earth Spectra

Solar and Atmospheric Radiation

Solar and Earth Emission

Absorption Bands by Atmospheric Trace Gases

Vertical Range of Solar Radiation

Source: http://amazing-space.stsci.edu

Solar Constant and Incoming Solar Radiation (Insolation)

● Solar constant at top of atmosphere:1364 W/m2

● Incoming solar radiation: 341 W/m2

● Why the factor of 4?

Radiative Energy Budget