Chapter 6: Blackbody Radiation: Thermal Emission

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?)


Earth-Atmosphere Energy Balance

Fig. 9.1


Molecules as Billiard Balls


Container of Photons: It really works!

Radiation Pressure I=T4, =5.67e-8 W m-2 K-4


DEFINITION OF THE BRIGHTNESS TEMPERATURE

TB

Measured Radiance at wavenumber v =Theoretical Radiance of a Black Body at temperature TB


FTIR Radiance: Atmospheric IR Window

13 microns 8 microns

Ground, Ts

FTIR


Ground, Ts

FTIR

FTIR Brightness Temperatures


Nimbus Satellite FTIR Spectrum

FTIR

Ground, Ts


Nimbus Satellite and Ground Based FTIR Spectrum

FTIR

Ground, Ts

Ground, Ts

FTIR

Ts

≈Ts


Planck Functions for Earth and Sun: Note some overlap (4 microns), but with log scale, can treat them

separately for the most part.


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.


Blackbody Radiation: A look at the Forms:


Blackbody Radiation: Another look at the Forms:


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.


Simple Model for Earth’s Atmosphere: No Absorption of Sunlight by the Atmosphere.


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


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


Radiative Equilibrium RelationshipsA = surface albedo≈0.3


of solar radiation




of IR radiation







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


Sufficient Number of Equations to Solve for All FluxesA = albedo ≈ 0.3


of solar radiation




of IR radiation







S0 = 1360 W/m2


Resulting Temperate Example for the Simple Model


Broad View of Model Predictions

SurfaceTemperature (K)

AtmosphereTemperature (K)

Yellow line follows Tsurface = 285 K.


Calculate the microwave radiant intensity (magnitude and polarization state) measured by a satellite above a

calm water surface.

55 deg Is

Ip


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


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


Reflectivity of Water And Ice: Normal Incidence

What drives the reflectivity?


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


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)


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!


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


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


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


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).


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?)


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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Chapter 6: Blackbody Radiation: Thermal Emission

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