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Lab Exercise 3 – Electro-magnetic Radiation (EMR) Principles
Purpose:
To reinforce and apply concepts of EMR and its interaction with
atmospheric constituents.
Materials:
Calculator
Please show all calculations to receive credit for answers. Be sure that all results are given in appropriate
units.
1. (A). What are the approximate/generalized wavelength ranges of the following spectral regions (in appropriate units of wavelength)?
(a) Ultraviolet = 0.01 – 0.4 mm
(b) Visible = 0.4 – 0.7 mm
(c) Near IR = 0.7 – 1.5 mm
(d) Shortwave IR = 0.7 – 3 mm
(e) Thermal IR = 3-14 mm
(f) Microwave > 1000 mm
(B). Rayleigh scattering occurs when particles are less than 1/10th the wavelength of the striking EMR.
What diameter particles (i.e. less than or equal to what particle diameters) would cause Rayleigh scattering in the following spectral regions? State diameters in microns (i.e., micrometers).
(a) Ultraviolet @ 0.30 microns = 0.1 * 0.30 = 0.03 microns
(b) Near IR @ 1.00 microns = 0.1 * 1.00 = 0.1 microns
(c) Visible light – blue @ 0.45 microns = 0.1 * 0.45 = 0.045 microns
(d) Visible light – red @ 0.65 microns = 0.1 * 0.65 = 0.065 microns
(e) How much more Rayleigh scattering occurs for blue light at 0.45 microns than near infrared energy
at 0.90 microns (assuming a uniform size-quantity distribution for atmospheric particles)?
Blue light (1/ (0.45)4) = 24.386 mm
Near infrared (1/ (0.90)4) = 1.524 mm
Which is mean 24.386 – 1.524 = almost 16 blue more than red in terms of Rayleigh scattering
2. Briefly define, describe and compare the relative difference between wavelength, frequency, photon energy,
and atmospheric transmission characteristics for the visible, near IR, and microwave portions of the EMR spectrum. Specify the frequency ranges for each of these three spectral regions (as you specified the wavelength
ranges in #1 above). Describe photon energy and atmospheric transmission characteristics in relative terms
(e.g., high, medium, low). A table is a convenient way to organize your response.
Wavelength
λ
Frequency
f
Photon Energy
Q
Medium
High
Medium High
Atm. Transmission
Visible
Low
Near IR
Medium
Low
Low
High
High
Low
Low
High
Microwave
ح
3. (A) Refer to the graph below, which depicts solar spectral irradiance at the atmosphere’s edge and at sea level.
Examining the general trend, which types of radiation correspond to the greatest differences between the two
irradiance curves, considering your answers from questions 1 (B) and 2 (table above) regarding scattering and
atmospheric transmission differences among short and long wavelengths? [Ignore the relatively short ranges in
the infrared where atmospheric transmission is low and linked to specific gases on the graph.]
3. (B) Building upon your answer to question 3(A), approximate the wavelength ranges where atmospheric
gases interfere strongly with transmission (deviations from the overall trend of higher scattering in shorter
wavelengths)? Do you think these wavelengths are more subject to scattering, or to absorption and/or reflectance by the relatively large gas molecules specified?
4. To improve radiometric resolution, passive microwave systems normally have low spatial resolution with
large instantaneous-field-of-view (IFOV; i.e., cannot resolve small targets). The natural irradiance level of microwaves is low as indicated by Planck's radiation law (Q= hf).
(a) What does this law mean in terms of controls on Q (photon energy) by EMR wavelength and frequency?
(b) Explain how this law relates to measurements in the microwave portion of the EMR spectrum (microwave radiometry) and why lower spatial resolution (i.e., larger IFOV) is beneficial for signal acquisition.
5. (a) If the solar irradiance at the top of the atmosphere in a given waveband is 200 Wm-2, the atmospheric
transmissivity is 0.85, and the radiation is incident from zenith, what is the irradiance at the surface?
Solar irradiance = > 200 w/m2
T = 0.85
Es= E * T
Es = (200) (0.85)
Es = 170 w/m2
(b) Given the same top of the atmosphere irradiance and waveband as in (a), what would the irradiance at the
surface be if the solar zenith angle () was 45 and atmospheric transmissivity at this incidence angle were
0.80?
Es = (E0) (T) (Cos0)
Es = (200 w/m2) (0.80) (cos 45)
ES = 113 w/m2
Electromagnetic Radiation (EMR):
Properties, Sources and Atmospheric
Interactions
EMR as Information Link
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Link between surface and sensor
Sun
Sensor
Surface
Energy Transfer
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Conduction
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Transfer of kinetic energy by collision of molecules/atoms
Requires direct contact
Energy Transfer (cont)
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Convection
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Kinetic energy of bodies is transferred by movement of the bodies
Applies only to liquids or gases (i.e., fluids)
Example: boiling water
Energy Transfer (cont)
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Radiation
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Energy transferred between objects in the form of electromagnetic
waves/particles (light)
Can occur in a vacuum (w/o a medium)
EMR Properties
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Wave Theory
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EMR => continuous wave
Energy transfer through media (vacuum, air, water, etc.)
Properties
Quantum (Particle) Theory
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EMR => packets of energy
Photons or quanta
Interaction of energy with matter
Wave Theory
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Explains energy transfer as a wave
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Energy radiates in accordance with basic wave theory
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Travels through space at speed of light
at
3 x 108 ms-1 (meters per second)
Light from the
Earth to the moon
Sun to Earth
Sun to Mercury
Sun to Venus
Sun to Mars
Sun to Jupiter
Sun to Saturn
Sun to Uranus
Sun to Neptune
Sun to Pluto
Sun to the nearest star
Sun to the furthest stars
Travel time
1.28 seconds
8.5 minutes
3 minutes
6 minutes
12.5 minutes
43 minutes
1 hour
2.6 hours
4 hours
5.4 hours
4.3 years
18 billion years
Electromagnetic Wave
Two components or fields
E = electrical wave
M = magnetic wave
http://www.colorado.edu/physics/2000/waves_particles/
Wave Properties
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Amplitude
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Height of the wave
Related to amount of energy carried by wave
Wavelength
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Distance between successive crests or troughs of wave
Measured in microns and designated by lambda (l)
Wave Properties (cont)
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Frequency
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Number of wave forms or oscillations passing through a given
point per unit time
Measured as cycle/second (cycle s-1) or Hertz (Hz)
Medium
High
Low
Wave Properties (cont)
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Refraction
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Bending of EMR waves due to change in medium
Change in medium -> change in density
-> change in velocity -> change in direction
air
water
Wave Properties (cont)
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Coherence
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Regular and systematic relationship between amplitudes of
two waves - waves are in phase
Incoherent if relationship between wave amplitudes is
random – waves are out of phase
Wave Properties (cont)
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Diffraction
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Change in direction (bending) of wave path due to coming in contact with a
solid object
Quantum Theory
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Wave theory doesn’t account for all properties of
EMR
Interaction of EMR with matter (atoms)
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Absorption
Emission
EMR is transferred in discrete packets (particles)
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Photons (quanta)
Quantum Theory (cont)
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Planck’s Law (energy of a quantum):
Q = hf
Where: Q = energy of a quantum in Joules [J]
h = Planck’s constant = 6.626 x 10-34 [J s]
f (or ) = frequency of EMR wave [cycles s-1]
or Hertz [Hz]
Electromagnetic Spectrum
l (mm = 10-6 m)
Ultraviolet
Near IR
Far IR
Microwave &
0.01 – 0.4 mm
0.7 – 1.5 mm
5.6 – 1000 mm
Radio > 1000 mm
Visible 0.4-0.7 mm
Mid IR 1.5-5.6 mm
Thermal-IR 3-14 mm
Wavelength & Frequency
Near Infrared
Green
Microwave
Wavelength and Frequency
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Relationship is inverse
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High frequency associated with short wavelengths and high
energy
Low frequency associated with long wavelengths and low
energy
c=lxf
where:
c = speed of light (3 x 108 m s-1)
l = wavelength
f = frequency
therefore: f = c/l
and
l = c/ f
EMR Spectrum
Short l, High f, High Q
Long l, Low f, Low Q
Wavelength and Frequency - Example
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Energy of Green Light
l = 0.5 mm = 0.5 x 10-6 m = 5 x 10-7 m
f = C/l = (3 x 108 m/s) / (5 x 10-7 m) = 0.6 x 1015 Hz
= 6 x 1014 Hz
Q = h f = 6.626 x 10-34 Js x 6 x 1014 cycles/s
= 39.756 x 10-20 J
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Energy of Microwave
l = 3000 mm = 3 x 10-3 m
f = C/l = (3 x 108 m/s) / (3 x 10-3 m) = 1 x 1011 Hz
Q = hf = 6.626 x 10-34 Js x 1 x 1011 cycles/s
= 6.626 x 10-23 J
Energy Laws
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Planck’s Radiation Law -- Total energy is a non-linear
function of temperature (T) and wavelength (l)
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The hotter the object, the more radiation emitted
The hotter the object, more radiation emitted in shorter
wavelengths
Sun
Earth
Energy Laws
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Stefan-Boltzmann Law quantifies total emitted radiation
from a blackbody as a function of temperature
M = sT4
Where M = total emitted radiation (Wm-2)
s = Stefan-Boltzmann constant = 5.6697 X 10-8 Wm-2 K-4
T = temperature (K)
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Blackbody - a hypothetical or ideal radiator that absorbs
and re-emits all energy incident upon it
Energy Laws (cont)
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Wien’s Displacement Law
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Used to identify wavelength of maximum energy emission (lmax)
Inversely related to temperature
lmax = k/T
Where
k = 2898 mK
T = temperature (K); K = Kelvin
Energy Laws (cont)
Sun: T = 6000K
lmax = 0.48m
Earth: T = 300K
lmax = 9.7m
Radiant Energy / Radiant Flux
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Radiant Energy (Ql)
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Capacity of radiation to do work
Radiant Flux (F)
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Amount of radiant energy onto, off of or through a surface per unit
time
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Measured in J/s or Watts (W)
Radiant Flux Density
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Amount of radiant energy onto, off of or through a surface per unit
time and area
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Measured in Watts per square meter (Wm-2)
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Irradiance = into surface; Exitance = away from surface
Radiometric Quantities
Name
Symbol
Units
Concept
Radiant
Energy
Ql
Joules (J)
Capacity of radiation within a
spectral band to do work
Radiant
Flux
Fl
Js-1,
Time rate of energy flow onto, off
of or through a surface
Irradiance
El
Wm-2
Fl incident upon a surface per
unit area of that surface
Radiant
Exitance
Ml
Wm-2
Fl leaving a surface per unit area
of that surface
Radiance
Ll
Watts (W)
Wm-2sr-1
Fl leaving a specific projected
source area, in a given direction,
w/in a specific solid angle
Partitioning of Energy at Surface
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Radiant flux at the surface is partitioned among:
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Absorption
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Transmission
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Reflection
Radiation Budget Equation
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Radiant Flux (F) incident at a surface = 1 + 2 + 3
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1) Amount of energy absorbed by the surface
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2) Amount of energy reflected from the surface
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3) Amount of energy transmitted through the surface
Radiation Budget Equation (cont.)
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Dimensionless ratios:
al = Fabsorbed / Fil
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Spectral absorptance:
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Spectral transmittance: tl = Ftransmitted / Fil
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Spectral reflectance:
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rl = Freflected / Fil
al + tl + rl = Fil = 1
Radiation Budget Equation (cont.)
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Proportion of energy absorbed/transmitted/reflected
will vary from target-to-target
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Material type
Material condition
For a given target, proportion absorbed, transmitted,
and reflected energy will vary with wavelength
Ability to distinguish between targets
Atmospheric Interactions
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Energy detected by sensor is a function of
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Atmospheric influences
Surface properties
Atmosphere will affect EMR in three ways
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Absorption
Transmission
Scattering
Constituents in the Atmosphere
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Responsible for absorption and scattering
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Water droplets/ice crystals
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Gas Molecules
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clouds
CO2, water vapor, ozone
Aerosols
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particles suspended in the atmosphere
smoke, dust, sea salt, chemical pollutants
Absorption
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Radiant energy is taken in by matter and
converted into other forms of energy
Atmospheric gases are selective absorbers
w/ reference to wavelength
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Significant Absorbers: Oxygen, Nitrogen,
Ozone, Carbon Dioxide, Water Vapor
◼ Ozone – ultraviolet region
◼ Water Vapor – specific bands in infrared
◼ Carbon Dioxide – thermal infrared region
EMR Transmission
Energy propagated directly through the atmosphere
T
T
T
A
A
A
Atmospheric Windows
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Portions of the spectrum that transmit radiant energy
effectively
Wavelength Window
Radiation Type
1.5 – 1.8 mm
2.0 – 2.4 mm
3.0 – 5.0 mm
8.0 – 14.0 mm
10.5 – 12.5 mm
> 0.6 cm
UV, visible, reflected IR (near)
Reflected IR (shortwave)
Reflected IR (shortwave)
Thermal IR
Thermal IR
Thermal IR
Microwave
*0.3 – 1.1 mm
*scattering may limit transmission for UV and shorter visible wavelengths
Scattering
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Re-direction of energy
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No change in other properties
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Three primary types
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1. Rayleigh (molecular)
2. Mie (aerosol)
3. Non-selective (particulates)
Rayleigh (Molecular) Scattering
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Radiation interacts with molecules/particles whose
diameter is much shorter than the wavelength
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Less than or equal to 1/10 the wavelength
Scattering is usually performed by atmospheric gasses
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Oxygen
Nitrogen
Rayleigh Scattering (cont)
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Amount of scattering is inversely proportional to
wavelength raised to 4th power (l-4)
I a l-4
Blue light (0.4 mm) → 1/ 0.44 = 39.0625
Near infrared (0.8 mm) → 1/ 0.84 = 2.4414
→ 39.0625 / 2.4414 = 16 times more scattering
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Accounts for:
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blue sky
red sunset
Rayleigh (cont)
Mie (Aerosol) Scattering
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Particles with diameter about equal to wavelength
d
d
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Dust, pollutants, volcanic eruptions, smoke
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Affects longer wavelengths than Rayleigh scattering
I a l-1
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Occurs in lower 4.5 km of atmosphere
Mie Scattering (cont)
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Direction/amount of scattering depends on physical
characteristics of the aerosol:
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Shape / size
Distribution of particles
Rayleigh vs. Mie Scattering
Non-Selective Scatter
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Diameter of particles is much larger than wavelength
(on order 10 x wavelength)
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Cloud water droplets/ice crystals are source
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Affects all wavelengths, hence “non-selective”
Scattering Effects
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Scatter can occur anywhere in information flow:
Sun -> Surface -> Sensor
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Reduces direct illumination from sun and creates
diffuse illumination
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Creates noise and reduces contrast in image
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May add to or reduce signal received by sensor
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Filters may be used to reduce effects of haze and
scatter
Path Radiance
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Radiation scattered into
the sensor from the
atmosphere
Mostly shorter
wavelengths
Path
radiance
Atmospheric Effects
Contrast Reduction
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Atmospheric effects can reduce image contrast
Summary
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Energy Flow
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Wave Theory
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Wave properties
Wavelength – Frequency relationship
Quantum Theory
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Conduction, Convection, Radiation
Energy of a photon
EMR spectrum
Summary
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Energy Levels
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Stefan-Boltzmann Law
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Wien’s Displacenment Law
Summary
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Atmospheric Constituents
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Absorption
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Reflection/Scattering
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Rayleigh (molecular)
Mie (aerosol)
Non-selective
Transmission (atmospheric windows)