chapter 6: blackbody radiation: thermal emission
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Pat Arnott, ATMS 749 Atmospheric Radiation Transfer
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/hbase/mod6.html
Eventual Absorption: Acts like a black body (classroom also?)
Pat Arnott, ATMS 749 Atmospheric Radiation Transfer
Earth-Atmosphere Energy Balance
Fig. 9.1
Pat Arnott, ATMS 749 Atmospheric Radiation Transfer
Molecules as Billiard Balls
Pat Arnott, ATMS 749 Atmospheric Radiation Transfer
Container of Photons: It really works!
Radiation Pressure I=T4, =5.67e-8 W m-2 K-4
Pat Arnott, ATMS 749 Atmospheric Radiation Transfer
DEFINITION OF THE BRIGHTNESS TEMPERATURE
TB
Measured Radiance at wavenumber v =Theoretical Radiance of a Black Body at temperature TB
Pat Arnott, ATMS 749 Atmospheric Radiation Transfer
FTIR Radiance: Atmospheric IR Window
13 microns 8 microns
Ground, Ts
FTIR
Pat Arnott, ATMS 749 Atmospheric Radiation Transfer
Ground, Ts
FTIR
FTIR Brightness Temperatures
Pat Arnott, ATMS 749 Atmospheric Radiation Transfer
Nimbus Satellite FTIR Spectrum
FTIR
Ground, Ts
Pat Arnott, ATMS 749 Atmospheric Radiation Transfer
Nimbus Satellite and Ground Based FTIR Spectrum
FTIR
Ground, Ts
Ground, Ts
FTIR
Ts
≈Ts
Pat Arnott, ATMS 749 Atmospheric Radiation Transfer
Planck Functions for Earth and Sun: Note some overlap (4 microns), but with log scale, can treat them
separately for the most part.
Pat Arnott, ATMS 749 Atmospheric Radiation Transfer
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.
Pat Arnott, ATMS 749 Atmospheric Radiation Transfer
Blackbody Radiation: A look at the Forms:
Pat Arnott, ATMS 749 Atmospheric Radiation Transfer
Blackbody Radiation: Another look at the Forms:
Pat Arnott, ATMS 749 Atmospheric Radiation Transfer
Earth’s Surface Temperature
Te Earth’s radiative temperatureTs Sun’s radiative temperatureRs Sun’s radiusRse Sun to Earth distancea Earth’s surface solar reflectancet IR transmittance of Earth’s atmosphere.
Pat Arnott, ATMS 749 Atmospheric Radiation Transfer
Simple Model for Earth’s Atmosphere: No Absorption of Sunlight by the Atmosphere.
Pat Arnott, ATMS 749 Atmospheric Radiation Transfer
Simple Surface Temperature Calculation Assuming Solar Absorption only at the surface, IR emission by the atmosphere and Earth’s
surface, and IR absorption by the Atmosphere.
S0 = 1376 W/m2=Solar Irradiance at the TOA and =Stefan-Boltzmann constant
Pat Arnott, ATMS 749 Atmospheric Radiation Transfer
Model with Atmosphere that absorbs solar radiation: Terrestrial IR=IR=LW, Solar = SW A = surface 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 .
Fluxes:
F1=incident from sun
F2 = tswF1 = (1-asw)F1
F3=Solar reflected to space by
the earth, atmosphere=F4
transmitted by atmosphere.
F4=Solar reflected by surface.
F8=IR emitted by surface.
F7=tlwF8=(1-alw)F8 .
F5=F6=IR emitted by atmosphere.
Solar Flux Relationships:
F1= S
F2 = tswF1 = (1-asw) F1= (1-asw) S
F4=A 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
Pat Arnott, ATMS 749 Atmospheric Radiation Transfer
Radiative Equilibrium RelationshipsA = surface 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 .
Fluxes:
F1=incident from sun
F2 = tswF1 = (1-asw)F1
F3=Solar reflected to space by
the earth, atmosphere=F4
transmitted by atmosphere.
F4=Solar reflected by surface.
F8=IR emitted by surface.
F7=tlwF8=(1-alw)F8 .
F5=F6=IR emitted by atmosphere.
Fnet,toa= F3+F5+F7-F1 = Flux (Out-In)=0
Fnet,surface= F4+F8-F2-F6 = Flux (Out-In)=0
Pat Arnott, ATMS 749 Atmospheric Radiation Transfer
Sufficient Number of Equations to Solve for All FluxesA = 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
Pat Arnott, ATMS 749 Atmospheric Radiation Transfer
Resulting Temperate Example for the Simple Model
Pat Arnott, ATMS 749 Atmospheric Radiation Transfer
Broad View of Model Predictions
SurfaceTemperature (K)
AtmosphereTemperature (K)
Yellow line follows Tsurface = 285 K.
Pat Arnott, ATMS 749 Atmospheric Radiation Transfer
Calculate the microwave radiant intensity (magnitude and polarization state) measured by a satellite above a
calm water surface.
55 deg Is
Ip
Pat Arnott, ATMS 749 Atmospheric Radiation Transfer
Fresnel Reflection Coefficients: What is the magnitude of the light specularly reflected from a surface? (Also can get the transmitted wave magnitude).
Medium 2
Medium 1
i
t
Pat Arnott, ATMS 749 Atmospheric Radiation Transfer
Reflectivity of Water And Ice
BrewsterAngle
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
Pat Arnott, ATMS 749 Atmospheric Radiation Transfer
Reflectivity of Water And Ice: Normal Incidence
What drives the reflectivity?
Pat Arnott, ATMS 749 Atmospheric Radiation Transfer
Fresnel Reflection Coefficients: What is the magnitude of the light specularly reflected from a surface? (Also can get the transmitted wave magnitude).
Medium 2
Medium 1
i
t
ICE
Transmission &
Absorption:Tp=1-Rp=ap=p
Ts=1-Rs =as=s
a=absorption coefficient
=emissivity
Pat Arnott, ATMS 749 Atmospheric Radiation Transfer
Calculate the microwave radiant intensity (magnitude and polarization state) measured by a satellite above a
calm water surface. The answer.
55 deg Is
Ip
Is0
Ip0
T
i
t
What are the sources of Ip0?
(same form for Is)
Pat Arnott, ATMS 749 Atmospheric Radiation Transfer
WHY?
What if ni = 0? Rp and Rs are not 0 in that case.
How could we get emission if ni=0?
We have no absorption in that case!
If ni=0, then abs=4ni/ = 0!
Pat Arnott, ATMS 749 Atmospheric Radiation Transfer
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 k2=0.
55 deg Is
Ip
Pat Arnott, ATMS 749 Atmospheric Radiation Transfer
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.
dz
z m
Pat Arnott, ATMS 749 Atmospheric Radiation Transfer
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.
dz
z
emissivity
boundary transmissivitymedium
propagator
m
Pat Arnott, ATMS 749 Atmospheric Radiation Transfer
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.
dz
zm
The main contribution to the emitted radiation comes fromabout a skin depth of the surface, /(4ni).
Pat Arnott, ATMS 749 Atmospheric Radiation Transfer
For problem 6.28, let Ip,s0=0. Calculate for each frequency.
55 deg Is
Ip
T
i
t (same form for Is)
N2
N1
Key for remote sensing:N2(T) (why?)
Pat Arnott, ATMS 749 Atmospheric Radiation Transfer
AMSR Sensor: http://wwwghcc.msfc.nasa.gov/AMSR/
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 02:54:58 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.
NASA A-Train
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