Transcript Introduction

Electromagnetic Spectrum
and Laws of Radiation
Satellite Meteorology/Climatology
Professor Menglin Jin
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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
satellite’s sensor?
Frequency and wavelength
Speed of light
Frequency (Hz)
v= c

Wavelength
1 hertz (Hz) = one cycle per second
c = 3.0 x 108 ms-1
Electromagnetic spectrum
Radio waves
1000m
Microwave
1m
Longer waves
Infrared (IR)
1000 m
1m
Ultraviolet (UV)
Red Orange
Green
Yellow
(0.7m) (0.6m)
(0.5m)
Visible
Blue
X rays
0.001m
Shorter waves
1,000,000 m = 1m
Violet
(0.4m)
Gamma
Blackbody radiation
Examine relationships between
temperature, wavelength and energy
emitted
 Blackbody: A “perfect” emitter and
absorber of radiation... does not exist
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Measuring energy
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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 
Radiance
Normal
to surface
Toward satellite
Solid angle, measured in steradians
(1 sphere = 4 sr = 12.57 sr)
Electromagnetic radiation
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Two fields:
• Electrical &
magnetic
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C=3*108=v * 
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Travel
perpendicular &
speed of light
Property &
behaves in
predictable way
Frequency &
wavelength
Photons/quanta
Stefan-Boltzmann Law
M BB = T 4
Total irradiance
Stefan-Boltzmann constant
emitted by a blackbody
(sometimes indicated as E*)
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
Planck’s 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:
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Planck’s 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
Planck curve
Wein’s 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 @ 300K: ~10 m
Sun @ 6000K: ~0.5 m
Intensity and Wavelength of Emitted Radiation :
Earth and Sun
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.
Emissivity and Kirchoff’s 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)
Kirchoff’s Law
Materials which are strong absorber at a particular
wavelength are also strong emitter at that wavelength
Solar Constant
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The intensity of radiation from the Sun
received at the top of the atmosphere
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Changes in solar constant may result in
climatic variations
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http://www.space.com/scienceastronomy/
071217-solar-cycle-24.html
Solar Constant
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While there are minor
variations in solar
output…
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the amount of solar
radiation at the top of the
Earth’s atmosphere is
fairly constant ~1367
W/m2.
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Its called the solar
constant
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The wavelengths we are most interested in for
climatology and meteorology are between
0.01 and 100 μm
Radiative Transfer
What happens to radiation (energy)
as it travels from the “target” (e.g.,
ground, cloud...) to the satellite’s
sensor?
Processes:
transmission
reflection
scattering
absorption
refraction
dispersion
diffraction
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!)
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reflection
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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.
Reflection from smooth surface
light ray
angle of
incidence
angle of
reflection
Scattering
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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.
Molecular scattering
(or other particles)
Scattering from irregular
surface
Absorption (attenuation)
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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.
incident
radiation
substance (air, water,
ice, smog, etc.)
absorption
transmitted
radiation
Refraction
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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.
Refraction in two different media
less dense
medium
more dense
medium
Gradually changing medium
low density
ray
wave
fronts
high density
Dispersion
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the process in which radiation is separated
into its component wavelengths (colors).
The “classic” example
prism
Diffraction
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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.
light
shadow
region
Solid object
Atmospheric Constituents:
empty space
molecules
dust and pollutants
salt particles
volcanic materials
cloud droplets
rain drops
ice crystals
Optical phenomena
light
process
+
atmospheric
constituent
optical
phenomena
atmospheric
structure
Atmospheric Structure
temperature gradient
humidity gradient
clouds
layers of stuff - pollutants, clouds
Remote sensing system
A technology used for
obtaining information about a
target through the analysis of
data acquired from the target
at a distance.
Applications
Atmospheric windows
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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 > 6 mm (MW)
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
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• Water vapor: 6.3m channel on GOES satellites
Where are the windows?
Windows for Space-based Remote Sensing
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Space-based remote sensors allow us to observe & quantify Earth’s
environments in regions of the electromagnetic spectrum to which our eyes
are not sensitive
Size parameter
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Type of scattering depends on size parameter ()
• Size parameter compares radiation wavelength to size of
scattering particles
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Mie scattering for 0.1 <  < 50 (radiation and scattering
particles are about same size)
Rayleigh scattering for  < 0.1 (scattering particles <<
than radiation)
Geometric optics for  > 50 (scattering particles >> than
radiation)
=
2r
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Radius of scattering particles
Size parameter
1e+05
1e+04
Geometric
r (m)
1e+03
1e+02
Mie
1e+01
1e+00
1e-01
Rayleigh
1e-02
No scattering
1e-03
1e-04
1e-01 1e+00 1e+01 1e+02 1e+03 1e+04 1e+05 1e+06
 (m)
Mie scattering
Scattering efficiency
for each scatterer
{
s() =   r2 Qs N(r) dr
Scattering coefficient
(similar to k in Beer’s
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
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
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
Beer’s Law
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The rate of decrease in intensity of radiation as it
passes through a medium is proportional to the
intensity of radiation
Flux density
after passing
medium
I
Io
Initial flux density
= exp (- x)
Extinction coefficient Distance in medium
• Extinction may be due to scattering or absorption
(scattering, absorption coefficients)
Beer’s Law for Air
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Must add density into equation
Density
Flux density
after passing
medium
I
Io
Initial flux density
= exp (-x)
Extinction coefficient Distance in medium
Beer’s Law: A more general form
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Absorption corss section gives the
“shadow” cast by each particles
Flux density
after passing
medium
Absorption cross section
(m2)
I
Io
Initial flux density
= exp (-n b x)
Number of particles
per sq. m (m-2)
Distance in medium
Inverse Squared Law
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Radiation from a spherical source (e.g.,
Sun) decreases with the square of the
distance
Final flux density
Initial flux density
E2 = E1 (R1 / R2 )2
Radius of emitter
(e.g., Sun)
Distance of target from
emitter (e.g., distance
of Earth from Sun)