ATMOSPHERIC RADIATION

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ATMOSPHERIC RADIATION S.K. Satheesh Centre for
Atmospheric Oceanic Sciences Indian Institute
of Science Bangalore.
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Part-1 BASIC CONCEPTS Basic introduction to
electromagnetic field Dual nature of
electromagnetic radiation Electromagnetic
spectrum Basic radiometric quantities energy,
intensity, and flux The Lambert-Beer law Concepts
of extinction (scattering absorption) and
emission Optical Depth
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Part-2 BLACKBODY RADIATION Concepts of a
blackbody and thermodynamical equilibrium Main
Laws Ø Planck function Ø Stefan-Boltzmann law Ø
Wiens displacement law Ø Kirchhoffs law
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Part-3 Atmospheric Scattering and Absorption
Rayleigh scattering, Mie scattering, Radiatively
active species Why sky is blue? Why sunset sky
is red? Simple aspects of Radiative Transfer
through the atmosphere What happens to short
wave radiation incident at the top of the
atmosphere? What happens to long wave
(terrestrial) radiation? Radiative
Balance? RADITION BUDGET
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Ways to label radiation

• By its source
• Solar radiation - originating from the Sun
• Terrestrial radiation - originating from the
  Earth
• By its proper name
• ultra violet, visible, near infrared, infrared,
  microwave, etc.
• By its wavelength
• short wave radiation ? ? 4 micrometers
• long wave radiation ? gt 4 micrometers

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BASIC CONCEPTS Basic introduction to
electromagnetic field Dual nature of
electromagnetic radiation Electromagnetic
spectrum Basic radiometric quantities energy,
intensity, and flux The Lambert-Beer law Concepts
of extinction (scattering absorption) and
emission Optical Depth
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BASIC INTRODUCTION TO ELECTROMAGNETIC
FIELD Electromagnetic radiation is a form of
energy Electromagnetic radiation is so-named
because it has electric and magnetic fields that
simultaneously oscillate in planes mutually
perpendicular to each other and to the direction
of propagation through space Electromagnetic
radiation has the dual nature its exhibits wave
properties and particulate properties
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Wave nature of radiation
The electric (E) and magnetic (H) fields
oscillate in the x-y plane and perpendicular to
the direction of propagation (z-direction) Waves
are characterized by wavelength (or frequency)
and speed.
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WAVE NATURE OF RADIATION A
schematic of a wave travelling in the z-direction
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The speed of light in a vacuum c 2.9979 x 108
m/s 3.0 x 108 m/s Wavelength is the
distance between two consecutive peaks or
troughs in a wave (symbolized by ?) Frequency
is defined as the number of waves (cycles) per
second that pass a given point in space
(symbolized by ?) Wavenumber is defined as a
count of the number of wave crests (or troughs)
in a given unit of length Since all types of
electromagnetic radiation travel at the speed of
light, short-wavelength radiation must have a
high frequency
Relation between ? and ? ? ? c
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UNITS Wavelength units length Angstrom (A)
1 A 10 -10 m Nanometer (nm) 1 nm 10 -9
m Micrometer (?m) 1 ?m 10 -6 m Frequency
units cycles per second 1/sec (or sec -1) is
called hertz (abbreviated Hz) Wavenumber units
inverse length (often in cm -1)
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PARTICULATE NATURE OF RADIATION Radiation can
be also described in terms of particles or
packets of energy, called photons The energy of
a photon is given by the expression where h is
Planks constant (h 6.6256x10 -34 J s). This
equation relates energy of each photon of the
radiation to the electromagnetic wave
characteristics (? and ?).
Ephoton h ? h c / ?
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COORDINATE SYSTEMS Both the Cartesian
coordinate system and spherical coordinate
system are used to characterize the propagation
of electromagnetic radiation Cartesian
(rectangular) coordinate system three orthogonal
unit vectors x, y, and z. Any vector A can be
expressed as Ax x Ay y Az z and its
magnitude is A A
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Spherical coordinate system distance r, the
zenithal (?) and azimuthal angles (?).
Spherical and rectangular coordinates are related
as x r sin(?) cos(?) y r sin(?) sin(?) z
r cos(?)
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Solid Angle is defined as the ratio of the area
of a spherical surface intercepted by the cone
to the square of the radius UNITS of a
solid angle steradian (sr) EXAMPLE Solid
angle of a sphere 4?R2 / R2 4?
R
? A / R2
A
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The electromagnetic spectrum of the sun
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Spectrum of the Sun compared with that of the
Earth
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Percent Spectral Distribution of Solar Energy
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BASIC RADIOMETRIC QUANTITIES Flux (or
irradiance) is defined as radiant energy per unit
time per unit wavelength (or frequency) range
per unit area perpendicular to the given
direction Thus monochromatic flux is the
integration of normal component of monochromatic
intensity over the all solid angles over the
hemisphere. UNIT J sec-1 m-2 ?m W m-2 ?m
F? dE? / dt dA d?
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Intensity (or radiance) is defined as radiant
energy in a given direction per unit time per
unit wavelength (or frequency) range per unit
solid angle per unit area perpendicular to the
given direction I? is referred to as
monochromatic intensity. Note Monochromatic
does not mean at a single wavelengths, but in a
very narrow (infinitesimal) range of wavelength
?? centered at ?. UNITS (J sec-1 m-2 ?m-1
sr-1 ) (W m-2 ?m-1 sr-1 )
I? dE? / d? dt dA d?
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PROPERTIES OF INTENSITY In general, intensity
is a function of the coordinates, direction,
wavelength (or frequency), and time. Thus it
depends on seven independent variables three in
space, two in angle, one in wavelength (or
frequency) and one in time. Intensity, as a
function of position and direction, gives a
complete description of the electromagnetic
field. If intensity does not depend on the
direction, the electro- magnetic field is said to
be isotropic. If intensity does not depend on
position the field is said to be homogeneous.
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Concept of Extinction (scattering absorption)
and Emission Electromagnetic radiation in the
atmosphere interacts with gases, aerosol
particles, and cloud particles. Extinction and
emission are two main types of the interactions
between an electromagnetic radiation field and a
medium (e.g., the atmosphere). Radiation is
emitted by all bodies that have a temperature
above absolute zero (often referred to as
thermal emission).
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General Definition of Extinction
Emission Extinction is a process that decreases
the radiant intensity, while emission increases
it. Extinction is due to absorption and
scattering. Absorption is a process that removes
the radiant energy from an electromagnetic field
and transfers it to other forms of
energy. Scattering is a process that does not
remove energy from the radiation field, but
redirect it.
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More on Extinction Scattering can be thought of
as absorption of radiant energy followed by
re-emission back to the electromagnetic field
with negligible conversion of energy. Thus,
scattering can remove radiant energy of a light
beam traveling in one direction, but can be a
source of radiant energy for the light beams
traveling in other directions. The fundamental
law of extinction is the Lambert-Beer law.
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Consider a small volume ?V of infinitesimal
length ds containing optically active matter.
Thus, the change of intensity along a path ds is
proportional to the amount of matter in the
path. For extinction For emission
where ?e is the volume extinction coefficient
(LENGTH-1) and J? is the source function.
dI? -?e I? ds
ds
I0
I
?V
dI? -?e J? ds
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In the most general case, the source function
has emission and scattering contributions. NOTE
Volume extinction coefficient is often referred
to as the extinction coefficient. Generally,
the volume extinction coefficient is a function
of position s.
Extinction coeff. Absorption coeff.
Scattering coeff.
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Optical Depth
Altitude
E2
E1
Surface
E1, E2, .. are extinction coefficients at each
altitude
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BLACKBODY RADIATION Concepts of a blackbody
and thermodynamical equilibrium Main Laws Ø
Planck function Ø Stefan-Boltzmann law Ø Wiens
displacement law Ø Kirchhoffs law Simple
aspects of Radiative Transfer through the
atmosphere
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Concepts of Blackbody A hypothetical body that
completely absorbs all wavelengths of radiation
incident on it. Such bodies do not reflect light,
and therefore appear black if their temperatures
are low enough so as not to be self-luminous.
All blackbodies heated to a given temperature
emit thermal radiation with the same spectrum
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PROPERTIES OF BLACKBODY RADIATION Radiation
emitted by a blackbody is isotropic, homogeneous
and unpolarized. Blackbody radiation at a given
wavelength depends only on the temperature
T. Any two blackbodies at the same temperature
emit precisely the same radiation. A blackbody
emits more radiation than any other type of an
object at the same temperature.
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RADIATION Basic Laws
Planks Law Intensity (or radiance) emitted by a
blackbody having a given temperature is given by
Planks Law. Planks Law can be expressed in
wavelength domains as, where ? is the
wavelength h is the Planks constant kB is the
Boltzmanns constant (kB 1.38 x 10-23 J K -1)
c is the velocity of light and T is the absolute
temperature of a blackbody.
B?(T) 2hc2 / ?5 (ehc/kBT?-1)
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Stefan-Boltzmann Law The
Stefan-Boltzmann law states that the total power
(energy per unit time) emitted by a blackbody,
per unit surface area of the blackbody, varies
as the fourth power of the temperature. where
is the Stefan-Boltzmann constant (? 5.671 x
10-8 W m-2 K-4), F is energy flux W m-2, and T
is blackbody temperature K.
F ? T4
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Wiens Displacement Law The Wiens
displacement law states that the wavelength at
which the blackbody emission spectrum is most
intense varies inversely with the blackbodys
temperature. The constant of proportionality is
Wiens constant (2897 K mm) where ? is the
wavelength (in micrometers, ?m) at which the
peak emission intensity occurs, and T is the
temperature of the blackbody (in degrees Kelvin,
K). NOTE this law is simply derived from,
NOTE The hotter the object the shorter the
wavelength of the maximum intensity emitted.
?max 2897 / T
?B? / ?? 0
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Wiens Displacement Law
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Kirchhoffs Law The Kirchhoffs law states
that the emissivity, ??, of a medium is equal to
the absorptivity, A?, of this medium under
thermo- dynamic equilibrium where ?? is
defined as the ratio of the emitting intensity to
the Planck function A? is defined as the ratio
of the absorbed intensity to the Planck
function. For a blackbody For a
non-blackbody For a gray body
?? A?
?? A? 1
?? ? A? lt 1
?? A? lt 1
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Kirchoffs Law
Day

• Objects that are good absorbers are also good
  emitters
• Consider a land surface
• During the day the land absorbs solar radiation
  and warms
• At night the land emits infrared radiation and
  cools relative to its surroundings

Warm
Land (warms due to solar radiation)
Night
Cool
Land (cools by IR radiation)
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Emissivity of Surfaces In general,
emissivity depends on the surface temperature,
wavelength and some physical properties of the
surface (e.g., the refractive index).
In thermal IR ( gt 4 ?m) , nearly all surfaces
are efficient emitters with the emissivity gt
0.8. Emissivity of some surfaces in the IR
region from 10 to 12 ?m Water 0.993-0.998 Ice
0.98 Green grass 0.975 - 0.986 Sand 0.949 -
0.962 Granite 0.898
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Reflection The Albedo of Various Surfaces

• Albedo the ratio of reflected radiation to
  incident radiation
• Surface albedo varies
• Spatially
• Temporally

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Basic Properties of Radiatively Active Species
(gases, aerosols, and clouds) Atmosphere is
composed of Ø Gases Ø Aerosols Ø Cloud
droplets. Atmospheric Gases Constant gases
Nitrogen, Oxygen, Argon, Neon, Helium, Krypton,
Xenon etc. Variable gases Water vapor, Carbon
dioxide, Methane, Hydrogen, Nitrous oxide, Carbon
monoxide, Ozone.
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Atmospheric Aerosols Atmospheric aerosols (or
particulate matter) are solid or liquid
particles or both suspended in air with
diameters between about 0.002 mm to about 100
mm. Aerosol particles vary greatly in sources,
production mechanisms, sizes, chemical
composition, amount, distribution in space
and time, and how long they survive in the
atmosphere (i.e. lifetime). Primary atmospheric
aerosols are particulates that emitted directly
into the atmosphere (for instance, sea-salt,
mineral aerosols (or dust), volcanic dust, smoke
and black carbon, etc). Secondary atmospheric
aerosols are particulates that formed in the
atmosphere by gas-to-particles conversion
processes (for instance, sulfates, nitrates,
some organics).
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Cloud Droplets Major characteristics are cloud
type cloud coverage cloud droplet
concentration cloud droplet size. Cloud droplet
sizes vary from a few micrometers to hundreds
of micrometers. Cloud droplet concentration
varies from about 10 cm-3 to 1000 cm-3 with
average droplet concentration of a few hundred
cm-3 . The liquid water content of typical
clouds, often abbreviated LWC, varies from
approximately 0.05 to 3 g (water) m-3 , with
most of the observed values in the 0.1 to 0.3 g
(water) m-3. NOTE Clouds cover approximately
50 of the Earths surface. Average global
coverage over the oceans is about 65 and over
the land is about 52.
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Atmospheric Scattering
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ATMOSPHERIC SCATTERING Any type of
elecromagnetic wave propagating through the
atmosphere is affected by the air molecules and
aerosols because of their interaction with
radiation namely (i) scattering (ii) absorption
and (iii) emission. Scattering occurs at all
wavelengths (spectrally not selective) in the
electromagnetic spectrum. Any material whose
refractive index is different from that of the
surrounding medium (optically inhomogeneous)
scatter radiation.
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More on Scattering Rayleigh and Mie
Scattering The amount of scattered energy depends
strongly on the ratio of particle size to
wavelength of the incident wave. When scatterers
are very small compared to the wavelength of
incident radiation (r lt ?/10), the scattered
intensity on both forward and backward
directions are equal. This type of scattering is
called Rayleigh scattering. For larger
particles (r gt ?), the angular distribution of
scattered intensity becomes more complex with
more energy scattered in the forward direction.
This type of scattering is called Mie scattering.
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R ltlt ?
R ? ?
R gtgt ?
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Single Scattering
? 2?R/?
What happens in the red box?
More scattering
a is like size of particle/l of light
Bigger particles compared to l
This graph shows the amount of scattering as a
function of the relative size of the scatterers
to the wavelength of light
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Elastic Scattering, Multiple Scattering In
Rayleigh and Mie scattering, both the scattered
and incident radiation have the same wavelength
and hence this two scattering process are called
Elastic Scattering. In the real atmosphere the
particles and air molecules are randomly
distributed and are separated by distances large
compared to their sizes. So each particle
scatter independently and there will not be any
interference between the separately scattered
waves. This is called Independent Scattering. In
the actual case of scattering in the atmosphere
there are chances that the scattered radiation
from one particle may have scattered again by
other particles. This is called Multiple
Scattering. Multiple scattering influences are
more in turbid or polluted atmospheres.
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Difference Between Scattering and
Absorption Both scattering and absorption remove
flux from an incident wave. During scattering
process flux is not lost from the incident beam
but is redistributed over the total solid angle
centered around the scatterer and it does not
change the internal energy states of the
molecules. Absorption changes the internal
energy states of the molecules. Absorption is
spectrally selective, scattering is not.
Scattering depends on the ratio of particle size
to wavelength of light.
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Theory of Scattering Assuming a scatterer, with
size R very small compared to wavelength of
incident radiation.
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Rayleigh Scattering Rayleigh scattered
intensity is given by, where ? is the
polarisability, ? is the wavelength of incident
beam and ? is the scattering angle. The angular
dependence of the scattered intensity is
specified using a parameter called PHASE FUNCTION
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Parallel component
Perpendicular component
Unpolarised
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Incident beam
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Why is the Sky Blue? Sunset Sky Red?
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Why is the day sky blue?

• Sunlight is scattered by air molecules
• Air molecules are much smaller than the lights l
• Shorter wavelengths (green, blue, violet)
  scattered more efficiently
• So the color we see is dominated by short visible
  wavelengths

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Why not violet? Since violet light (0.405 ?m)
has a shorter wavelength than the blue, why then
doesn't the sky appear violet? This is because
the energy contained in the violet spectrum is
much smaller than that contained in the blue
spectrum and also human eye has a much lower
response to the violet colour.
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droplets
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Why are sunsets red?

• The sun appears fairly white when its high in
  the sky
• Near the horizon, sunlight must penetrate a much
  greater atmospheric path
• More scattering
• Scattering by gases removes short visible ls
  from the line-of-sight
• Sun appears orange/yellow because only longer
  wavelengths make it through
• When particle concentrations are high, the
  slightly longer yellow ls are also scattered
• - Sun appears red/orange

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cloud
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Solar Radiation
Terrestrial Radiation
N2O
O2 and O3
CO2
H2O
The Electromagnetic Spectrum and Absorbing Gases
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Atmospheric Windows

• Portions of the electromagnetic spectrum where
  atmospheric gases absorb relatively little energy
• Visible Wavelengths
• 8-12 micrometers in the terrestrial band

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SIMPLE ASPECTS OF ATMOSPHERIC RADIATIVE TRANSFER
Sun
Earth
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What happens to short wave radiation incident at
the top of the atmosphere?

• It can be absorbed by the atmosphere
• It can be reflected by clouds, particles and air
  molecules back to space
• It can be transmitted to the surface
• where it can be
• absorbed
• reflected back upward into the atmosphere
• some of this may be absorbed by the atmosphere
• some may be transmitted through the atmosphere
  back to space

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What happens to long wave (terrestrial)
radiation?

• The earth's surface emits LW radiation
• Some of this radiation escapes directly through
  the atmosphere to space, thus cooling the planet.
• Some is absorbed by gases and clouds in the
  atmosphere. 
• The atmospheric gases and clouds emit LW
  radiation in all directions.
• The atmosphere's LW emission downward "warms" the
  surface.
• The atmosphere's LW emission upward joins that
  from the surface escaping to space, thus cooling
  the planet.

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Clear sky Short wave region, Incident light 1
unit, Single scattering, One layer From
Lambert-Beer Law, I I0exp(-k? m), ? where m
slant path optical depth / vertical optical
depth Transmittance transmitted energy /
incident energy Thus transmittance I / I0
exp(-k? m) Major scatterers Air molecules
(Rayleigh), Aerosols (Mie) Major Absorbers
Ozone, Water Vapour, CO2, O2 etc.
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We define the following parameters. ?R
transmittance due to Rayleigh scattering ?A
transmittance due to aerosol scattering
absorption ?M transmittance due to molecular
absorption TOTAL TRANSMITTANCE OF THE DIRECT
BEAM IN THE ATMOSPHERE, All the above
transmittances are wavelength dependent
? ?R ?A ?M
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Origin of Diffuse Radiation Diffuse radiation
is originated by scattering of the light due to
air molecules and aerosols. In our case, since
I0 1 unit Ground reaching radiation, I
? The balance, I0 - I I0 - I0 ? I0 (1-?)
is lost in the atmosphere due to scattering and
absorption. Since, I0 1 unit, the energy lost
(1-?)
I0
Transmittance ?
I I0 ?
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Considering a Rayleigh atmosphere, the diffuse
radiation due to Rayleigh scattering (1-?R)
Considering an atmosphere with only aerosols,
the diffuse radiation due to aerosol scattering
?(1-?A) where ? is the single scattering
albedo. ? scattering / (scattering
absorption) In a real atmosphere, Rayleigh
scattered diffuse radiation (1-?R) ?A ?M
Aerosol scattered diffuse radiation ?(1-?A) ?R
?M
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Air molecules scatter (Rayleigh) equally in
forward and backward directions where as for
aerosols the ratio of forward to backward
scattering depends on a parameter namely,
FORWARD SCATTERANCE. Forward scatterance is the
ratio of energy scattered in the forward
direction to total energy scattered Direct
radiation at the surface ?R ?A ?M Diffuse
radiation at the surface 0.5(1-?R) ?A ?M
Fc?(1-?A) ?R ?M
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Sun
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Radiative balance? If the earth always radiates
energy, why doesnt it cool? It is in a state
of radiative equilibrium. Incoming radiation is
balanced by outgoing radiation. At what
temperature is this equilibrium reached for the
earth system? 255 K. Radiative equilibrium
predicts surface temperature of 255 K or -18
degrees C. But, the earths observed average
surface temperature is 15 C. Why? The answer
lies in an understanding of absorption,
reflection, transmission of radiation.
S0/4 (1-?) ?T4
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Annual Radiation Budget - Short Wave Detail
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Thank you