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Electromagnetic Spectrum and Laws of Radiation

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How much energy is emitted by some medium? ... Twilight ... Absorption corss section gives the 'shadow' cast by each particles = exp (-n b x) I ... – PowerPoint PPT presentation

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Title: Electromagnetic Spectrum and Laws of Radiation


1
Electromagnetic Spectrum and Laws of Radiation
  • Satellite Meteorology/Climatology
  • Professor Menglin Jin

2
  • How much energy is emitted by some medium?
  • What kind of energy (what frequency/wavelength)
    is emitted by some medium?
  • What happens to radiation (energy) as it travels
    from the target (e.g., ground, cloud...) to the
    satellites sensor?

3
Frequency and wavelength
Speed of light
c
v
Frequency (Hz)
??
Wavelength
1 hertz (Hz) one cycle per second c 3.0 x 108
ms-1
4
Electromagnetic spectrum
Red (0.7?m)
Orange (0.6?m)
Yellow
Green (0.5?m)
Blue
Violet (0.4?m)
Visible
Ultraviolet (UV)
Gamma
X rays
Infrared (IR)
Microwave
Radio waves
0.001?m
1?m
1000 ?m
1m
1000m
Longer waves
Shorter waves
1,000,000 ?m 1m
5
Blackbody radiation
  • Examine relationships between temperature,
    wavelength and energy emitted
  • Blackbody A perfect emitter and absorber of
    radiation... does not exist

6
Measuring energy
  • Radiant energy Total energy emitted in all
    directions (J)
  • Radiant flux Total energy radiated in all
    directions per unit time (W J/s)
  • Irradiance (radiant flux density) Total energy
    radiated onto (or from) a unit area in a unit
    time (W m-2)
  • Radiance Irradiance within a given angle of
    observation (W m-2 sr-1)
  • Spectral radiance Radiance for range in ?

7
Radiance
Toward satellite
Normal to surface
Solid angle, measured in steradians (1 sphere
4? sr 12.57 sr)
8
Electromagnetic radiation
  • Two fields
  • Electrical magnetic
  • Travel perpendicular speed of light
  • Property behaves in predictable way
  • Frequency wavelength
  • Photons/quanta

C3108v ?
9
Stefan-Boltzmann Law
M BB ??T 4
Total irradiance emitted by a blackbody (sometimes
indicated as E)
Stefan-Boltzmann constant
The amount of radiation emitted by a blackbody is
proportional to the fourth power of its
temperature Sun is 16 times hotter than Earth
but gives off 160,000 times as much radiation
10
Plancks Function
  • Blackbody doesn't emit equal amounts of radiation
    at all wavelengths
  • Most of the energy is radiated within a
    relatively narrow band of wavelengths.
  • The exact amount of energy emitted at a
    particular wavelength lambda is given by the
    Planck function

11
Plancks function
First radiation constant
Wavelength of radiation
c1?-5
B ? (T)
exp (c2 / ?T ) -1
Absolute temperature
Second radiation constant
Irridance Blackbody radiative flux for a single
wavelength at temperature T (W m-2)
Total amount of radiation emitted by a blackbody
is a function of its temperature c1
3.74x10-16 W m-2 c2 1.44x10-2 m K
12
Planck curve
13
Weins Displacement Law
?mT 2897.9 ?m K
Gives the wavelength of the maximum emission of
a blackbody, which is inversely proportional
to its temperature Earth _at_ 300K 10 ?m Sun _at_
6000K 0.5 ?m
14
Intensity and Wavelength of Emitted Radiation
Earth and Sun
15
Rayleigh-Jeans Approximation
B? (T) (c1 / c2) ??-4 T
When is this valid 1. For temperatures
encountered on Earth 2. For millimeter and
centimeter wavelengths At microwave wavelengths,
the amount of radiation emitted is directly
proportional to T... not T4
B? (T)
TB
(c1 / c2) ??-4
Brightness temperature (TB) is often used for
microwave and infrared satellite data,
where it is called equivalent blackbody
temperature. The brightness temperature is equal
to the actual temperature times the
emissivity.
16
Emissivity and Kirchoffs Law
??????????????
Actual irradiance by a non-blackbody at
wavelength ?
Emittance Often referred to as emissivity
Emissivity is a function of the wavelength of
radiation and the viewing angle and) is the ratio
of energy radiated by the material to energy
radiated by a black body at the same temperature
????E???absorbed/ E???incident?
Absorptivity (r? , reflectivity t? ,
transmissivity)
17
Kirchoffs Law
Materials which are strong absorber at a
particular wavelength are also strong emitter at
that wavelength
18
Solar Constant
  • The intensity of radiation from the Sun received
    at the top of the atmosphere
  • Changes in solar constant may result in climatic
    variations
  • http//www.space.com/scienceastronomy/071217-solar
    -cycle-24.html

19
Solar Constant
  • While there are minor variations in solar output
  • the amount of solar radiation at the top of the
    Earths atmosphere is fairly constant 1367 W/m2.
  • Its called the solar constant

20
  • The wavelengths we are most interested in for
    climatology and meteorology are between 0.01 and
    100 µm

21
Radiative Transfer
  • What happens to radiation (energy) as it travels
    from the target (e.g., ground, cloud...) to the
    satellites sensor?

22
Processes
  • transmission
  • reflection
  • scattering
  • absorption
  • refraction
  • dispersion
  • diffraction

23
transmission
  • the passage of electromagnetic radiation through
    a medium
  • transmission is a part of every optical phenomena
    (otherwise, the phenomena would never have
    occurred in the first place!)

24
reflection
  • the process whereby a surface of discontinuity
    turns back a portion of the incident radiation
    into the medium through which the radiation
    approached the reflected radiation is at the
    same angle as the incident radiation.

25
Reflection from smooth surface
light ray
angle of reflection
angle of incidence
26
Scattering
  • The process by which small particles suspended in
    a medium of a different index of refraction
    diffuse a portion of the incident radiation in
    all directions. No energy transformation
    results, only a change in the spatial
    distribution of the radiation.

27
Molecular scattering (or other particles)
28
Scattering from irregular surface
29
Absorption (attenuation)
  • The process in which incident radiant energy is
    retained by a substance.
  • A further process always results from absorption
  • The irreversible conversion of the absorbed
    radiation goes into some other form of energy
    (usually heat) within the absorbing medium.

30
incident radiation
substance (air, water, ice, smog, etc.)
transmitted radiation
absorption
31
Refraction
  • The process in which the direction of energy
    propagation is changed as a result of
  • A change in density within the propagation
    medium, or
  • As energy passes through the interface
    representing a density discontinuity between two
    media.

32
Refraction in two different media
less dense medium
more dense medium
33
Refraction in two different media
less dense medium
Dt
more dense medium
Dt
34
Gradually changing medium
low density
ray
wave fronts
high density
35
Dispersion
  • the process in which radiation is separated into
    its component wavelengths (colors).

36
The classic example
white light
prism
37
Diffraction
  • The process by which the direction of radiation
    is changed so that it spreads into the geometric
    shadow region of an opaque or refractive object
    that lies in a radiation field.

38
light
shadow region
Solid object
39
Atmospheric Constituents
  • empty space
  • molecules
  • dust and pollutants
  • salt particles
  • volcanic materials
  • cloud droplets
  • rain drops
  • ice crystals

40
Optical phenomena
light
atmospheric constituent
optical phenomena

process
atmospheric structure
41
Atmospheric Structure
  • temperature gradient
  • humidity gradient
  • clouds
  • layers of stuff - pollutants, clouds

42
Optical phenomena
light
atmospheric constituent
optical phenomena

process
atmospheric structure
43
White clouds
  • scattering off cloud droplets 20 microns

44
Dark clouds
  • scattering and attenuation from larger cloud
    droplets and raindrops

45
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46
Blue skies
  • scattering from O2 and N2 molecules, dust
  • violet light is scattered 16 times more than red

47
Molecular scattering (nitrogen and oxygen)
  • blue scatters more than red

48
Hazy (milky white) sky
  • Scattering from tiny particles
  • terpenes (hydrocarbons) and ozone

49
Orange sun (as at sunset or sunrise)
  • Scattering from molecules
  • This is the normal sunset we see frequently

50
Red sun (as at sunset or sunrise)
  • Scattering from molecules, dust, salt particles,
    volcanic material
  • At 4 elevation angle, sun light passes through
    12 times as much atmosphere as when directly
    overhead

51
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52
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53
Green or blue sun
  • Scattering from volcanic ash, dust, smoke
  • uniform-sized particles

54
Twinkling (scintillation)
  • Refraction by small-scale temperature and
    relative humidity fluctuations

55
Twilight
  • Scattering and refraction by molecules and
    refractive index changes (air density decreases
    with altitude)

56
Back to remote sensing...
57
Remote sensing system
Applications
A technology used for obtaining information about
a target through the analysis of data acquired
from the target at a distance.
58
Atmospheric windows
  • Atmospheric window An electromagnetic region
    where the atmosphere has little absorption and
    high transmittance
  • Absorption channel An electromagnetic region
    where the atmosphere has high absorption
  • Atmospheric windows
  • Visible and Near IR wavelengths
  • 3.7 and 8.5-12.5 ?m (IR) 2-4 and gt 6 mm (MW)

59
Atmospheric windows
  • Atmospheric windows are useful for gathering
    information about the surface of the Earth and
    clouds
  • Absorption channels are useful for gathering
    information about atmospheric properties
  • Water vapor 6.3?m channel on GOES satellites

60
Where are the windows?
61
Windows for Space-based Remote Sensing
  • Space-based remote sensors allow us to observe
    quantify Earths environments in regions of the
    electromagnetic spectrum to which our eyes are
    not sensitive

62
Size parameter
  • Type of scattering depends on size parameter (?)
  • Size parameter compares radiation wavelength to
    size of scattering particles
  • Mie scattering for 0.1 lt ? lt 50 (radiation and
    scattering particles are about same size)
  • Rayleigh scattering for ? lt 0.1 (scattering
    particles ltlt than radiation)
  • Geometric optics for ? gt 50 (scattering particles
    gtgt than radiation)

2?r
Radius of scattering particles
?
?
63
Size parameter
Geometric
? 50
? 1
? 10-1
Mie
r (?m)
? 10-3
Rayleigh
No scattering
? (?m)
64
Mie scattering
Scattering efficiency for each scatterer

?s(?) ? ? r2 Qs N(r) dr
Scattering coefficient (similar to k in
Beers equation)
Radius of scattering particles
Number density of scatterers
Scattering efficiency depends on the type of
scatterer Number density is number of scatterers
for some unit volume with some range in sizes
65
Rayleigh scattering
?s(?) ? r2 Qs N
Number density (no concern for range in sizes)
Qs can be solved explicitly, as a function of the
size parameter
66
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67
Beers Law
  • The rate of decrease in intensity of radiation as
    it passes through a medium is proportional to the
    intensity of radiation
  • Extinction may be due to scattering or absorption
    (scattering, absorption coefficients)

Flux density after passing medium
I??
exp (-? x)
Io
Initial flux density
Extinction coefficient
Distance in medium
68
Beers Law for Air
  • Must add density into equation

Density
Flux density after passing medium
I??
exp (-????x)
Io
Initial flux density
Extinction coefficient
Distance in medium
69
Beers Law A more general form
  • Absorption corss section gives the shadow cast
    by each particles

Absorption cross section (m2)
Flux density after passing medium
I??
exp (-n b x)
Io
Initial flux density
Number of particles per sq. m (m-2)
Distance in medium
70
Inverse Squared Law
  • Radiation from a spherical source (e.g., Sun)
    decreases with the square of the distance

E2 E1 (R1 / R2 )2
Final flux density
Radius of emitter (e.g., Sun)
Distance of target from emitter (e.g.,
distance of Earth from Sun)
Initial flux density
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