Transcript 2 - Fundamentals (PPT-IIa)

REMOTE SENSING
EM Radiation Interactions
with the Atmosphere
Professor Ke-Sheng Cheng
Department of Bioenvironmental Systems Engineering
National Taiwan University
Propagation of EM radiation in
the atmosphere
• Once the electromagnetic radiation emitted by
the Sun enters into and propagates through
the Earth’s atmosphere, the atmosphere may
affect its properties including the speed and
direction of propagation, the wavelength, the
intensity, and the spectral distribution.
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• These effects arise due to absorption,
refraction, and scattering by the atmosphere.
• Most remote sensing image analysts are not
concerned about refraction, and thus we will
focus our discussion on details of absorption
and scattering by the atmosphere.
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Absorption
• Absorption is the process by which radiant
energy is absorbed and converted into other
forms of energy. An absorption band is a
range of wavelengths (or frequencies) in the
electromagnetic spectrum within which
radiant energy is absorbed by substances
such as water (H2O), carbon dioxide (CO2),
oxygen (O2), ozone (O3), and nitrous oxide
(N2O).
• Ozone, carbon dioxide, and water vapor are
the three main atmospheric constituents
which absorb radiation.
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• Ozone serves to absorb the harmful (to most
living things) ultraviolet radiation from the
sun. Without this protective layer in the
atmosphere our skin would burn when
exposed to sunlight.
• Carbon dioxide is referred to as a greenhouse
gas. This is because it tends to absorb
radiation strongly in the far infrared portion
of the spectrum - that area associated with
thermal heating - which serves to trap this
heat inside the atmosphere.
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• Water vapor in the atmosphere absorbs much
of the incoming longwave infrared and
shortwave microwave radiation (between 22
m and 1mm ). The presence of water vapor
in the lower atmosphere varies greatly from
location to location and at different times of
the year. For example, the air mass above a
desert would have very little water vapor to
absorb energy, while the tropics would have
high concentrations of water vapor (i.e. high
humidity).
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• Absorption is limited to radiation in certain
wavelength regions only. The wavelength
ranges in which the atmosphere is
particularly transmissive of energy are
referred to as atmospheric windows.
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Atmospheric Windows
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• Note also that heat energy emitted by the
Earth corresponds to a window around 10
m in the thermal IR portion of the spectrum,
while the large window at wavelengths
beyond 1 mm is associated with the
microwave region.
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Absorption of the Sun's Incident Electromagnetic Energy in the
Region from 0.1 to 30 m by Various Atmospheric Gases
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Major Atmospheric Windows
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Atmospheric absorption
• Absorption is the process by which radiant
energy is absorbed and converted into other
forms of energy. When propagating through
the earth atmosphere, photons of solar
radiation may be absorbed by constituent
molecules in the atmosphere.
• The molecular absorption involves three major
mechanisms including electron orbital
transition, molecular vibration, and molecular
rotation.
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• The energy required for electron orbit
transitions typically corresponds to energy
carried by photons of shortest wavelength
radiation in the ultraviolet and visible regions
of the electromagnetic spectrum.
• Energy change due to molecule vibration
motion is associated with absorption in the
near and middle infrared wavelength regions.
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• Energy change due to molecular rotation
motion is associated with absorption in the
thermal infrared and microwave wavelength
regions.
• Since a molecule possesses energy at certain
energy levels, it can only absorb energy of
certain incremental amount. Thus, we expect
atmospheric absorption to occur in selective
discrete wavelengths associated with those
photons having exact energy needed to induce
an allowable energy transition.
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• In fact, a few factors including the Heisenberg
uncertainty principle, the Doppler broadening
effect, and the pressure (or collision)
broadening effect contribute to the
broadening of these discrete absorption lines.
• The broadening effects result in spectral
absorption bands in the electromagnetic
spectrum.
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• Many near-by and overlapped absorption
bands can form a continuous wavelength
range in which radiant energy is significantly
absorbed by various atmospheric
constituents. Table 1.3 lists the main
absorption lines of the earth’s atmosphere.
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Table 1.3 Principal molecular absorption lines of the earth’s atmosphere.
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• Propagation of electromagnetic radiation in
the atmosphere can be conceived of as a
beam of photons bombarding a volumetric
sample of atmospheric particles.
• Most of the incoming photons pass through
the volume without colliding with
atmospheric particles, while a few photons
do collide with and are absorbed by
particles in the volume.
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Modeling the atmospheric absorption
- Absorption cross section
• The absorption cross section is a measure for
the probability of an absorption process. In
other words, absorption cross section
indicates the ability of an atmospheric
molecule to absorb a photon of a particular
wavelength.
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• It is expressed as a fraction of the geometric
cross section Cg that absorption by the
molecule takes place, i.e.,
C  Cg  r 2
where  is a wavelength-dependent efficient
factor that is proportional to the molecule’s
ability to absorb incoming photons.
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A beam of photons of a particular wavelength  coming into contact with a
set of m molecules of radius r in a volumetric element of cross section area
dA and length dx. A fraction of these photons are absorbed by these
molecules.
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• Let N(x) and N(x+dx) respectively represent
the number of photons of the same
wavelength  entering and leaving the
volumetric element per unit of time. The
number of photons absorbed by molecules in
the volumetric element per unit of time is
thus expressed as
 mC 
dN ( x)  N ( x  dx)  N ( x)   N ( x)
dx
 dAdx 
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• The amount of m/(dAdx) in the above equation
represents the number of molecules per unit
volume, i.e. the number density  of molecules.
Thus,
mC
dAdx
 C  
is termed the volumetric absorption coefficient .
It is worthy to note that, although the
absorption cross section C has a unit of area, it
does not refer to an actual area size.
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dN ( x)   N ( x) dx
dN ( x)
   ( x)dx
N ( x)
• The effect of atmospheric absorption can also
be expressed in terms of the radiant flux
absorbed by the volumetric element per unit
of time, i.e.,
d( x)
   ( x)dx
( x)
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Layered atmosphere
• Consider the atmosphere as having N
homogeneous layers.
Fig. 1.10 A stratified atmosphere with N homogeneous layers.
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• Considering all constituents present in the
atmosphere, the optical depth of the i-th
layer is calculated by
n
 i ( )  Zi   j ( )
j 1
where n is the number of different
constituents in that layer of the atmosphere.
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• Transmittance of the whole atmosphere with
respect to irradiance of wavelength  is given
by
N
N
 ( )   i ( )  e
i 1
i 1
  i (  )
e

N
i ( )
i 1
e
 a (  )
where  i ( ) and  a ( ) respectively represent
the transmittance of the i-th homogeneous
layer and the absorption optical depth of the
atmosphere as a whole.
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• If the irradiance has an incident angle , then
the optical depth of the entire atmosphere
due to absorption becomes


 a ( )  sec     i ( ) 
 i 1

N
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Table 1.4 Spectral regions commonly used in earth remote sensing.
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Atmospheric scattering
• Atmospheric particles: gas molecules, dust,
smoke, pollen, cloud droplets, raindrops, etc.
– These particles vary in their geometric shapes and
sizes.
• When propagating through the atmosphere,
solar radiation may be unpredictably
redirected (scattered) into various directions
by these atmospheric particles.
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• Major types of atmospheric scattering
– Rayleigh scattering
– Mie scattering
– Non-selective scattering
• The size of atmospheric particles relative to
wavelength of incident radiation affects the
occurrence of different scattering types.
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• The degree of scattering effect depends on
several factors
– the wavelength of radiant energy,
– the abundance of particles or gases, and
– the distance the radiant flux travels through the
atmosphere.
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Table 1.5 Types of atmospheric particles and their associated scattering
regimes with respect to visible, thermal infrared and microwave radiation.
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• Since the type of scattering that may occur is
dependent on the size of atmospheric
particles relative to the wavelength of
incident radiation, a size parameter  is
defined as
2r
 

where r is the radius of an atmospheric
particle and  is the wavelength of the
incident radiation.
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Fig. 1.12 Scattering regimes classified by the size parameter. VIS: visible,
NIR: near infrared, TIR: thermal infrared, MW: microwave.
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Rayleigh scattering
• Rayleigh scattering occurs when the diameter
of atmospheric particles (usually gas
molecules such as oxygen and nitrogen) are
much smaller than the wavelength of the
incident EM radiation.
• Similar to the absorption coefficient in the
atmospheric absorption process, scattering
coefficient of the atmospheric scattering can
also be defined.
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• The fractional amount of energy of spectral
wavelength  scattered into a direction defined
by  and  per unit solid angle per unit length is
defined as the Rayleigh angular scattering
coefficient and can be written as
where n is the wavelength-dependent index of
refraction of the atmosphere and m is the
number of gas molecules per unit volume. It is
noteworthy that Rayleigh angular scattering
coefficient does not depend on .
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Fig. 1.13 Radiation scattered into a direction defined by  and .
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• The total fractional amount of energy
scattered by gas molecules per unit length can
thus be calculated by integrating  r over all
angular directions, i.e.
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• The amount of scattered energy by Rayleigh
scattering is inversely proportional to the
fourth power of wavelength of radiation.
• Rayleigh scattering causes shorter
wavelengths of radiation to be scattered
much more than longer wavelengths.
• The blue sky and red sunset are typical
examples of Rayleigh scattering.
• Rayleigh scattering is the dominant scattering
mechanism in the upper atmosphere.
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• The effect of Rayleigh scattering varies with
the angle .
• The maximum amount of energy is scattered
into the incident ray direction.
• A phase function p() defined by
 r ( )
3
2

p( ) 
 1  cos  
 r ( ) 4  4
is used to characterize such angular variation
of the Rayleigh scattering.
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• The term r ( ) / 4 in the above equation
represents the average scattered fraction of
incident radiation per unit solid angle per
unit length.
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Fig. 1.14 Phase function of the Rayleigh angular scattering coefficient.
(Particle radius r=0.5nm, incident radiation wave length  = 0.45m (blue),
0.55m (green), 0.65m (red), unpolarized). The amount of scattered
radiation is linearly proportional to the distance from the center.
Energy scattered
into the direction
perpendicular to
the incident
radiation is the
lowest and
equals half of the
energy scattered
into the incident
direction.
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Mie scattering
• Mie scattering occurs when the size of
atmospheric particles such as smoke, haze,
pollen and dust is about the same order as
the wavelength of incident radiation. Mie
scattering occurs mostly in the lower portions
of the atmosphere where larger particles are
more abundant, and dominates when cloud
conditions are overcast.
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Fig. 1.15 Phase function of the Mie angular scattering coefficient. (Particle
radius r=0.5m, incident radiation wave length  = 0.45m (blue), 0.55m
(green), 0.65m (red), unpolarized). The amount of scattered radiation is
linearly proportional to the distance from the center.
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Non-selective scattering
• Nonselective scattering occurs when the
particles are large compared to the
wavelength of solar radiation. The effect of
nonselective scattering is approximately the
same in all scattering directions and is almost
independent of wavelength. This is why fog
and clouds appear white.
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Geometric scattering
• Geometric scattering occurs when the size of
atmospheric particles is much larger than the
wavelength of radiation. For geometric
scattering, ray tracing techniques can be
applied to describe the reflection and
refraction of solar radiation by these
particles.
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• Similar to the Rayleigh scattering, we can also
define angular scattering coefficient for the
Mie scattering and nonselective scattering.
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Estimating the exoatmospheric
irradiance by Langley plot
Es  E0 cos  i 1 ( )  E0 cos  i e
 (  ) sec  Z
ln Es  ln E0   ( ) sec Z
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Langley Plot
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