Chapter 6: Blackbody Radiation: Thermal Emission

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Chapter 6 Blackbody Radiation Thermal Emission
"Blackbody radiation" or "cavity radiation"
refers to an object or system which absorbs all
radiation incident upon it and re-radiates energy
which is characteristic of this radiating system
only, not dependent upon the type of radiation
which is incident upon it. The radiated energy
can be considered to be produced by standing wave
or resonant modes of the cavity which is
radiating. http//hyperphysics.phy-astr.gsu.edu/hb
ase/mod6.html
Eventual Absorption Acts like a black body
(classroom also?)
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Earth-Atmosphere Energy Balance
Fig. 9.1
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Molecules as Billiard Balls
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Container of Photons It really works!
I?T4, ?5.67e-8 W m-2 K-4
Radiation Pressure
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DEFINITION OF THE BRIGHTNESS TEMPERATURETB
Measured Radiance at wavenumber v
Theoretical Radiance of a Black
Body at temperature TB
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FTIR Radiance Atmospheric IR Window
13 microns
8 microns
FTIR
Ground, Ts
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FTIR Brightness Temperatures
FTIR
Ground, Ts
8
Nimbus Satellite FTIR Spectrum
FTIR
Ground, Ts
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Nimbus Satellite and Ground Based FTIR Spectrum
FTIR
Ts
Ground, Ts
Ts
FTIR
Ground, Ts
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Planck Functions for Earth and Sun Note some
overlap (4 microns), but with log scale, can
treat them separately for the most part.
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Eye Response Evolved to Match Solar Spectrum
Peak? The answer depends on how you look at the
distribution functions, wavelength or wavenumber.
Seems to support it
Seems not to support it.
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Blackbody Radiation A look at the Forms
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Blackbody Radiation Another look at the Forms
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Earths Surface Temperature
Te Earths radiative temperature Ts
Suns radiative temperature Rs Suns
radius Rse Sun to Earth distancea
Earths surface solar reflectancet IR
transmittance of Earths atmosphere.
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Simple Model for Earths Atmosphere No
Absorption of Sunlight by the Atmosphere.
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Simple Surface Temperature Calculation Assuming
Solar Absorption only at the surface, IR emission
by the atmosphere and Earths surface, and IR
absorption by the Atmosphere.
S0 1376 W/m2Solar Irradiance at the TOA and
?Stefan-Boltzmann constant
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Model with Atmosphere that absorbs solar
radiation Terrestrial IRIRLW, Solar SW

• A surface albedo0.3
• asw Atmosphere absorption of solar
  radiation
• tsw Transmission of solar by the
  atmosphere (1-asw)
• alw Atmosphere absorption of IR
  radiation
• Atmospheric Emissivity.
• tlw Transmission of IR by the atmosphere
  (1-alw)
• Ts surface temperature
• Ta atmosphere temperature
• 1 IR surface emissivity .
• Fluxes
• F1incident from sun
• F2 tswF1 (1-asw)F1
• F3Solar reflected to space by the earth,
  atmosphereF4 transmitted by atmosphere.
• F4Solar reflected by surface.
• F8IR emitted by surface.
• F7tlwF8(1-alw)F8 .
• F5F6IR emitted by atmosphere.

Solar Flux Relationships F1 S F2
tswF1 (1-asw) F1 (1-asw) S F4A F2 A (1-asw)
S F3 (1-asw) F4 A(1-asw)2 S
IR Flux Relationships F5 F6 alw ?Ta4
F8 ? ?Ts4 ?Ts4 F7 (1-alw) F8 (1-alw) ?Ts4
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Radiative Equilibrium Relationships

• A surface albedo0.3
• asw Atmosphere absorption of solar
  radiation
• tsw Transmission of solar by the
  atmosphere (1-asw)
• alw Atmosphere absorption of IR
  radiation
• Atmospheric Emissivity.
• tlw Transmission of IR by the atmosphere
  (1-alw)
• Ts surface temperature
• Ta atmosphere temperature
• 1 IR surface emissivity .
• Fluxes
• F1incident from sun
• F2 tswF1 (1-asw)F1
• F3Solar reflected to space by the earth,
  atmosphereF4 transmitted by atmosphere.
• F4Solar reflected by surface.
• F8IR emitted by surface.
• F7tlwF8(1-alw)F8 .
• F5F6IR emitted by atmosphere.

Fnet,toa F3F5F7-F1 Flux (Out-In)0 Fnet,surf
ace F4F8-F2-F6 Flux (Out-In)0
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Sufficient Number of Equations to Solve for All
Fluxes

• A albedo 0.3
• asw Atmosphere absorption of solar
  radiation
• tsw Transmission of solar by the
  atmosphere (1-asw)
• alw Atmosphere absorption of IR
  radiation
• Atmospheric Emissivity.
• tlw Transmission of IR by the atmosphere
  (1-alw)
• Ts surface temperature
• Ta atmosphere temperature
• 1 IR surface emissivity .
• S0 1360 W/m2

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Resulting Temperate Example for the Simple Model
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Broad View of Model Predictions
Surface Temperature (K)
Atmosphere Temperature (K)
Yellow line follows Tsurface 285 K.
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Calculate the microwave radiant intensity
(magnitude and polarization state) measured by a
satellite above a calm water surface.
Ip
55 deg
Is
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Fresnel Reflection Coefficients What is the
magnitude of the light specularly reflected from
a surface? (Also can get the transmitted wave
magnitude).
?i
Medium 1
Medium 2
?t
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Reflectivity of Water And Ice
Brewster Angle
Microwave ?15,000 microns nr 6.867192 ni
2.630
Mid Visible (green) ?0.5 microns nr
1.339430 ni 9.243 x 10-10
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Reflectivity of Water And Ice Normal Incidence
What drives the reflectivity?
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Fresnel Reflection Coefficients What is the
magnitude of the light specularly reflected from
a surface? (Also can get the transmitted wave
magnitude).
ICE
?i
Medium 1
Medium 2
?t
Transmission Absorption Tp1-Rpap?p Ts1-Rs
as?s aabsorption coefficient ?emissivity
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Calculate the microwave radiant intensity
(magnitude and polarization state) measured by a
satellite above a calm water surface. The answer.
Ip0
Ip
?i
Is0
55 deg
Is
What are the sources of Ip0?
T
?t
(same form for Is)
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WHY?
What if ni 0? Rp and Rs are not 0 in that
case. How could we get emission if ni0? We
have no absorption in that case! If ni0, then
?abs4?ni/? 0!
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The transmitted wave, with absorption k2,
diminishes. The total amount of radiation
eventually absorbed in medium 2 is given by Tp,s
(1 - Rp,s). No matter-filled medium exists
where k20.
Ip
55 deg
Is
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See how it goes for normal incidence Layer dz
emits radiation dI at temperature T that
transfers to the satellite. After emission, it is
partially absorbed in distance z, and then
transmitted out the boundary.
m
z
dz
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See how it goes for normal incidence Layer dz
emits radiation dI at temperature T that
transfers to the satellite. After emission, it is
partially absorbed in distance z, and then
transmitted out the boundary. Interpretation of
the terms.
boundary transmissivity
medium propagator
emissivity
m
z
dz
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See how it goes for normal incidence Layer dz
emits radiation dI at temperature T that
transfers to the satellite. After emission, it is
partially absorbed in distance z, and then
transmitted out the boundary. The total emission
is determined by integration in the z direction.
m
z
dz
The main contribution to the emitted radiation
comes from about a skin depth of the surface,
?/(4?ni).
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For problem 6.28, let Ip,s00. Calculate ? for
each frequency.
Ip
?i
55 deg
Is
Key for remote sensing N2(T) (why?)
N1
N2
T
?t
(same form for Is)
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AMSR Sensor http//wwwghcc.msfc.nasa.gov/AMSR/
NASA A-Train
In support of the Earth Science Enterprise's
goals, NASA's Earth Observing System (EOS) Aqua
Satellite was launched from Vandenberg AFB,
California on May 4, 2002 at 025458 a.m.
Pacific Daylight Time. The primary goal of Aqua,
as the name implies, is to gather information
about water in the Earth's system. Equipped with
six state-of-the-art instruments, Aqua will
collect data on global precipitation,
evaporation, and the cycling of water. This
information will help scientists all over the
world to better understand the Earth's water
cycle and determine if the water cycle is
accelerating as a result of climate change. The
Advanced Microwave Scanning Radiometer - EOS
(AMSR-E) is a one of the six sensors aboard Aqua.
AMSR-E is passive microwave radiometer, modified
from the Advanced Earth Observing Satellite-II
(ADEOS-II) AMSR, designed and provided by JAXA
(contractor Mitsubishi Electric Corporation). It
observes atmospheric, land, oceanic, and
cryospheric parameters, including precipitation,
sea surface temperatures, ice concentrations,
snow water equivalent, surface wetness, wind
speed, atmospheric cloud water, and water vapor.