Download Radiation in a Medium

Radiative Transfer – An Overview
Acknowledgements
• http://cimss.ssec.wisc.edu/goes/comet/radiative_transfer.html
• www.weatherchaos.umd.edu/classpresentations/Hudson_Intro_rad_trans.ppt
• http://timeforchange.org/radiation-wavelength-andgreenhouse-effect
Outline
• What is radiative transfer?
• Why should I care?
• How does it work?
Definition
• Radiative transfer (RT) is the study of how
radiation interacts with a medium.
• If you specify the characteristics of the medium
and the boundary (external illumination)
conditions, RT theory allows you to predict the
resulting radiation field.
Just Solve Maxwell’s
Equations, Right?
• Yes and no – the RT equation can be derived
entirely from Maxwell’s equations.
• But for atmospheric applications, a number of
simplifying assumptions can be made that
eliminate the need to work from first principles:
1. Far field, time-averaged solutions are sought.
2. Medium is sparsely populated with discrete,
randomly-oriented and randomly-placed
particles
Statistics
• The RT equation offers a statistical description of
the radiation field.
• Exact knowledge of the location of every particle
is not necessary.
• Prediction of the fate of each individual photon is
impossible, but photons are plentiful, so a
statistical description is robust.
• Bulk properties (number density, pressure,
temperature) are sufficient to describe the medium.
Neither Scalar nor Vector
• Some atmospheric variables are scalars (singlevalued for each point in space). Examples:
Temperature, pressure, density.
• Others are vectors (single value and direction
associated with each point in space). Example:
Wind speed.
• Radiation field has a single value for each
direction and each point in space.
Why Bother?
• All atmospheric processes are driven by solar
energy. Radiative transfer explains how this
energy is distributed throughout the atmosphere.
• The vast majority of our information concerning
the atmospheric state is derived from radiation
measurements. These measurements cannot be
properly interpreted without appreciating the
interaction between the atmosphere and the
radiation field.
Properties of EM radiation
• Oscillating electric and magnetic fields cause
energy to flow through space
• All EM radiation travels at the same speed c:
(assuming
8 m
c  2.9979  10
vacuum)
s
• 2 related properties of EM radiation are the
wavelength λ and the frequency ν:
c  
Electromagnetic spectrum
Energy Packets
• EM radiation is carried in individual “packets”
called photons:
E  h
• h = Planck’s constant = 6.626 × 10-34 J•s
• All matter emits radiation, due to thermal
vibrations
• Hot objects vibrate more energetically, and
produce higher-energy photons than cold objects.
Radiance
• Radiance is a radiation variable that describes the
brightness at a given point, in a given direction:
4
d E
SpectralRa diance 
dtdAdd
• A diffuse (multi-directional) radiation field must
be described by the radiance.
• Add up contributions from all wavelengths for the
radiance
Irradiance
• Irradiance is a radiation variable that describes
the energy flowing through a specified surface
(with a particular orientation) at a given point:
3
d E
SpectralIrradiance 
dtdAd
• The irradiance can result from mono-directional
beams, or from a collection of diffuse beams.
• Again, the for the total energy, use the integrated
quantity (irradiance).
Blackbodies…
• “Blackbody radiation” represents the maximum
radiation that a body at a particular temperature T
can emit at each wavelength:
Irradiance  T
4
2c 2 h
SpectralIrradiance  B 
hc

5
 exp(
)  1
kT


• k = Boltzmann’s constant = 1.381 × 10-23 J/K
Sun and Earth’s blackbody intensity
100 MW / m2 / μm (at λ = 0.5 μm) translates to
~ 2.5 × 1023 photons / s / m2 / nm)
…and Non-Blackbodies
• The emission by any body can be related to the
blackbody emission through the emissivity ελ:
EmittedRadiance(T ,  )
 
B.B.Emission (T ,  )
• ελ represents the efficiency of the emission process
for the specified body
• Can vary enormously across the spectrum (ex:
snow is black in the IR (ελ ~ 1), but white in the
visible (ελ ~ 0).
UV-VISIBLE SOLAR SPECTRUM
Radiation in a Medium
• Radiation incident upon a medium can be:
1. Absorbed (photon is converted to another form of
energy). Efficiency of absorption is described by
the absorptivity aλ:
AbsorbedRa diance( )
a 
IncidentRa diance( )
Radiation in a Medium
2. Reflected (photon leaves the medium in the
direction opposite the incident beam). Efficiency
of reflection is described by the reflectivity rλ:
Re flectedRadiance( )
r 
IncidentRa diance( )
Radiation in a Medium
3. Transmitted (photon leaves the medium in the
same direction as the incident beam). Efficiency
of transmission is described by the transmissivity
tλ:
TransmittedRadiance ( )
t 
IncidentRa diance( )
• From conservation of energy, a  r  t  1
Radiation at a Surface
• Radiation incident upon an opaque surface is
described the same way, except that transmission
is impossible, leaving:
a  r  1
(again from conservation of energy).
Earth Radiation Budget
a  r  1
Kirchhoff’s Law
• The efficiency of the emission and absorption
processes are related through Kirchhoff’s Law,
which states that:
 a


under conditions of “local thermodynamic
equilibrium” (LTE).
• LTE conditions prevail when the absorbers collide
frequently enough to effectively re-distribute the
absorbed energy, so that the subsequent emission
is related to the bulk T of the medium.
Please Don’t
Misunderstand…
• Kirchhoff’s Law does not imply that emission
and absorption are equal at all wavelengths (under
LTE conditions). It only implies that emission
and absorption are equally efficient at all
wavelengths (under LTE conditions).
• For example, high-energy solar photons may be
strongly absorbed (aλ ~ 1) in the atmosphere,
implying that the atmosphere emits the maximum
possible amount at that λ (ελ ~ 1)… but if T is low,
that may produce a negligible amount of energy.
Sources and Sinks
Sources
Emission
Sinks
Absorption
--------Scattering -------
• Scattering redirects the radiation beam, without
adding or removing energy. So the sink for one
direction becomes the source for another.
Scattering is All Relative
Rayleigh Scattering
• Describes the case for which the scatterer is much
smaller than the wavelength of the incident
radiation.
• Probability of scattering is proportional to λ-4.
• Scattering pattern depends upon the scattering
angle Θ as (1 + cos2Θ), so it varies by a factor of
2 between minimum (at Θ = 90º) and maximum
(at Θ = 0º or Θ = 180º).
Mie Scattering
• General expression for scattering by dielectric
spheres.
• Needed to describe scattering by a scatterer that is
the same size or larger than the wavelength of the
incident radiation.
• Probability of scattering is proportional to λ-1
(roughly).
• Scattering pattern is greatly elongated towards
forward scattering.
Phase diagrams for aerosols
Optical Thickness
• Radiative unit of length
• The probability P that a photon will pass
through a specified medium without
interaction with it (absorption or scattering) is
given by:
P  exp(  )
where τ = the “optical thickness” of the
medium.
Radiative Transfer Equation
dI 
 J  I
d 
• Iλ = spectral radiance
• Jλ = “source function”
• Jλ accounts for the possibility of photons added
to a particular line of sight, due to emission
and/or scattering
• Infrared RT and UV/visible RT are nearly
distinct specialties, due to the differences in
the physics involved.
UV/vis Radiative Transfer
• Atmospheric emission is negligible; Jλ is
entirely due to scattering.
• Absorption events change the electronic states
of the molecules.
• Absorption features tend to be broad.
Infrared Radiative Transfer
• Atmospheric scattering (by molecules) is
negligible; Jλ is entirely due to emission.
• Absorption events change the vibrationalrotational states of the molecules.
• Absorption features tend to be a forest of
narrow, closely-spaced absorption lines.
Greenhouse Effect
Greenhouse Effect
• Without our atmosphere, the surface
temperature of Earth would be ~ 255 K. The
natural greenhouse effect makes our planet
inhabitable for humans.
• Water vapor is the strongest greenhouse gas.
• We enhance this natural effect when we inject
additional gases that absorb in the infrared
(CO2, CH4, N2O, CFCs, …).
Greenhouse Effect
• Without our atmosphere, the surface
temperature of Earth would be ~ 255 K*. The
natural greenhouse effect makes our planet
inhabitable for humans.
• Water vapor is the strongest greenhouse gas.
• We enhance this natural effect when we inject
additional gases that absorb in the infrared
(CO2, CH4, N2O, CFCs, …).
Greenhouse Effect
Radiative forcing of long-lived greenhouse gases, relative to 1750
(From http://www.esrl.noaa.gov/gmd/aggi/, by Hoffman, 2007)
Volcanic Stratospheric Aerosol Cooling
Thanks to Makiko Sato:
http://www.giss.nasa.gov/data/strataer/
THE END