1. 8. Atmospheric Radiation
8.1 Basic concept and definition
8.2 Radiation laws
8.3 Radiative transfer equation
8.4 Solar radiation (Shortwave radiation)
8.5 Infrared radiation (Longwave radiation)
8.6 Radiation budget

2. 8.1 Basic concepts and definitions
Electromagnetic radiation:
* Energy propagated in the form of an advancing electric and
magnetic field disturbance.
* Travels in wave form at the speed of light (c).
* Wavelength ( ) is the physical distance between adjacent
maxima or minima in the electric or magnetic field. unit:
* Wave number ( ) is the number of wavelengths in a unit
distance, i.e., unit: 1/cm
* Frequency ( ) is the number of successive maxima or
minima passing a fixed point in a unit of time,
unit: cycle-per-second (cps) or 1/s

3. * The energy associated with electromagnetic radiation is
contained in discrete packets called photons.
* The energy contained in a photon is proportional to
frequency, and is given by
where h is Planck’s constant,

4. 2. Electromagnetic spectrum:
* Classified into bands
in terms of frequency
(or wavelength)
* Most significant spectral
regions associated with
radiative energy transfer
in atmosphere lie
between ultraviolet light
and microwaves.

5. 3. Solid angle
The ratio of the area of the sphere intercepted by the cone to the square of the radius
Units: Steradians (sr)
What is the area cut out of a sphere by one steradian?
What is the solid angle representing all directions at a point?

6. A meteorological satellite circles the earth at a height h above the earth’s
surface. Let the radius of the earth be and show that the solid angle
under which the earth is seen by the satellite sensor is

7. 4. Radiometric quantities
Radiant Flux: rate of energy transfer by electromagnetic radiation
Energy/time (J/s or Watt)
Irradiance: Radiant flux per unit area.
Monochromatic irradiance
W/m2
Radiance: Irradiance per unit solid angle.
Defines the irradiance coming from a particular direction.
W/(m2 steradian)

9.  = transmitted/incident = spectral transmittance
5. Absorption
a = absorbed/incident = spectral absorptance
r = reflected/incident = spectral reflectance
 = transmitted/incident = spectral transmittance
a + r +  = 1

10. 6. Scattering
* A physical process by which a particle in the path of an
electromagnetic wave continuously abstracts energy from
the incident wave and reradiates that energy in all directions.
* Gas molecules
Aerosols
Water droplets
Ice crystals
Large raindrops and hails
* Small particle: scatter light, equally in forward and backward directions
Larger particle: scatter more in forward direction, more complex

11. * Size parameter: * Multiple scattering
The ratio of the particle circumference to the incident wavelength
is the particle radius.
Rayleigh scattering:
<< 1
Lorenz-Mie scattering:
* Multiple scattering
Scattering more than once, important
process for the transfer of radiant
energy when aerosols and clouds
are involved.

12. A result of scattering plus absorption, which
* Extinction:
A result of scattering plus absorption, which
removes energy from a beam of light traversing
the medium and the light beam is attenuated.
Why does grass look green?
Why is the sky blue?

13. Planck’s Law 8.2 Radiation laws (blackbody) * Blackbody
all incident radiation is completely absorbed.
In all ’s, the maximum possible emission is realized.
The radiation is isotropic.
* The amount of radiation emitted is uniquely determined by temperature.
Planck’s law.
* Relate the emitted intensity to the wavelength and the
temperature of emitting substance.
* Rayleigh-Jeans distribution:
Wien distribution:

17. Stefan-Boltzmann Law Total radiant intensity emitted by a blackbody.
Integrate Planck’s law over all wavelengths.
Blackbody irradiance.
F =  T4
: Stefan-Boltzmann constant

18. Wein’s Displacement Law
Wavelength of maximum intensity
m = 2897/T,
units: m (m), T (K)
Allows brightness temperature to be inferred from the radiation emitted by an object

19. Kirchhoff’s Law
A molecule which absorbs radiation of a particular wavelength also is able to emit radiation of the same wavelength.
Rate of emission is a function of temperature and wavelength
Consider:
Two parallel plates of infinite extent (wall 1 and wall 2)
Both plates are at the same temperature.
Radiative transfer must be same in all directions.
Wall 1 has an absorptance a1 = 1

20. Absorptivity ( ) and emissivity ( )
Kirchoff’s law:
strong emitters  strong absorbers
weak emitters  weak absorbers
* Non-blackbodies absorb less radiation than do blackbodies.
* The ratio of absorbed monochromatic irradiance to blackbody
absorbed monochromatic irradiance is known as absorptivity.
* Non-blackbodies emit less radiation than do blackbodies.
* The ratio of emitted monochromatic irradiance to blackbody
monochromatic irradiance is known as emissivity.
* For a non-blackbody (or a gray body),
the Stefan-Boltzmann law is

21. Practice Problem
The average irradiance of solar radiation reaching the earth’s orbit is 1380 W/m2. Nearly all the radiation is emitted from the outer-most visible layer of the sun, which has a mean radius of 7x108 m. Calculate the equivalent blackbody temperature of this layer? The mean distance between the earth and sun is 1.5 x1011 m.

22. Practice Problem
Calculate the equivalent blackbody temperature of the earth, assuming a planetary albedo of Assume that the earth is in radiative equilibrium, so that there is no net energy gain or loss due to radiation.
Planetary albedo  the fraction of the total incident solar radiation that is reflected back into space without absorption.

23. Meteorology 342
Homework (8)
1. a) Find the equivalent blackbody temperature of Mars. Assume the irradiance at the top of the earth’s
atmosphere is , the distance from the earth to the sun is , the distance from
Mars to the sun is , and that Mars has an albedo of 0.17.
b) Justify your answers to a) are correct by comparing your values to the solar irradiance at the earth
and the radiative temperature of the earth.
2. An infrared scanning radiometer aboard a meteorological satellite measures the outgoing radiation
emitted from the earth’s surface in the window region. Assuming that the effect of the atmosphere
between the satellite and the surface can be neglected, what would be the temperature of the surface
if the observed radiance at is ?
3. A black land surface with temperature of emits radiation at all frequencies. What would be
the emitted radiance at , , and 31.4 GHz? Use appropriate Planck functions in
the calculations.
4. Assuming the average normal body temperature is , what would be the emittance of the body?
If it is not a blackbody but absorbs only 90% of the incoming radiation averaged over all wavelengths,
what would be the emittance in this case? Also, at which wavelength does the body emit the maximum
energy?

24. 8.3 Radiative transfer equation
1. The equation of radiative transfer
* Reduction of the radiant intensity due to absorption
* Increase in the radiant intensity due to emission and multiple scattering
: mass extinction cross section

25. 2. Beer-Bouguer-Lambert Law
The decrease in the radiant intensity traversing a homogeneous
extinction medium is in accord with the simple exponential function
whose argument is the product of the mass extinction cross section
and the path length.
Optical depth:
3. Schwarzschild’s equation
* The increase in the radiant intensity arising from blackbody
emission of the material.
* Reduction of the radiant intensity due to absorption

26. 8.4 Solar radiation (Shortwave radiation)
1. An energy source: the Sun
* Composed mostly of hydrogen (75% by mass) and
helium (25%), with traces of iron, silicon, neon, and
carbon
* Solar interior
a. Core:
Temperatures of 15 million K,
Density as high as 160,000 kg/m
Extends to about ¼ of the radius of sun
Thermonuclear reactions generate gamma- and x-rays
Sun produces radiation in its high density core 3

28. b. Radiative zone
Temperatures on the order of 100,000 K
Extends to about 0.85 of solar radius
Photons are continually absorbed and emitted
Photons are of longer and longer wavelengths
Takes 100,000 years for energy to make its way from
the core to the surface
c. Convective zone
Outermost 15%
Very opaque to radiation
Large radial temperature gradient
Convective currents carry energy from radiative zone to surface

29. * Solar atmosphere a. Photosphere The visible part of the sun
Very thin (~500km)
Where most of suns radiation is emitted
Temperature of about 6000K
Granular in appearance (because of convection)
b. Chromosphere
Rarefied (low density) layer
A couple of thousand kilometer thick

30. * Sunspots c. Corona Very rarefied
Very high temperature (up to 5 million K)
d. Above the corona is the magnetosphere.
e. The solar wind is a flow of atomic particles into space
from the sun
* Sunspots
* Sunspots are cool regions on the surface of the sun
Temperatures are ~4000 K, as compared with the normal 6000 K
* Sunspots are associated with a magnetic field disturbance

31. * Sunspots vary according to the sunspot cycle
11-year cycle: maximum in number of spots every 11 years or so,
with spots having the opposite polarity from the previous maximum
22-year cycle: this is the average time between maxima having the
same polarity
* When sunspots are present, the sun is very active in terms of
solar flares.

32. 2. The earth’s orbit around the sun
* All of the planets of the solar system revolve in elliptic orbits around
the sun, which is one of the foci of the ellipses.
* All of the planets except Mercury and Pluto orbit nearly in the same
plane, known as the ecliptic.
* The eccentricity of the earth’s orbit is currently about , so it is
very close to being a circle.
The average earth-sun distance is defined as an astronomical unit (AU)
and has a value of 149,597,870 km.
The earth is farthest from the sun (1.0167AU) at aphelion, which occurs
near July 4.
The earth is closest to the sun (0.9833AU) at perihelion, which occurs
near January 2.

33. * The earth wobbles on its axis due to precession. This precession
* The rotational axis of the earth is tilted at an angle of 23.5 degree
relative to the normal to the plane of the ecliptic
* The earth wobbles on its axis due to precession. This precession
changes the position in the orbit where the equinoxes and solstices
occur.
* The precession of equinoxes, the changing eccentricity of the orbit,
and the changing tilt of the rotational axis all affect the climate of
the earth.
The climate changes noted due to these factors are called Milankovitch
cycles after the astronomer who studied these climate oscillations.

34. angle to change from day-to-day throughout the year.
* The fact that the earth’s rotational axis is tilted causes the noon sun
angle to change from day-to-day throughout the year.
* Declination : the latitude over which the sun is directly overhead
The declination varies from 23.5 to degree over the course of one year
* Hour angle : the angle through which the earth must spin to bring
the sun directly over your longitude
* Solar zenith angle : the angle that the sun makes with the local vertical
The solar zenith angle can be found at any time by knowing the sun’s
declination, hour angle, and your latitude (south latitudes and
declinations are negative).
Sun angle: :
the angle that the sun makes
with the horizon

35. * Local noon is defined as the time that the sun crosses the local longitude (h=0)
* The changing sun angle has three effects:
1) Spreads the sun energy over a larger area when the sun angle is small,
2) Causes the rays to pass through more atmosphere (greater optical depth)
when the sun angle is small,
3) Results in varying lengths of daylight and darkness throughout the year.

36. Example: Compute the solar elevation angle at solar noon at the poles,
and the equator. Also computer the length of the day
(in terms of hours) at the equator and at at the equinox and solstice.

37. 3. Solar constant: Solar Spectrum
The total solar irradiance reaching the top of the earth’s atmosphere
on a surface perpendicular to the solar beam at the mean distance
between the sun and the earth.
Solar Spectrum
The recently proposed solar constant is about It varies with the
irradiance from the sun and changes with the sunspot cycle, but it doesn’t
vary by much.

38. The solar constant value is critical in the interpretation of
measured solar absorption and heating rates in the
atmosphere.
Two methods for determining the solar constant:
1) Satellite measurement with self-calibrating radiometers
2) Ground-based radiometers
Making use of Beer-Bouguer-Lambert law

39. 4. Solar insolation
Insolation is defined as the solar irradiance on a horizontal area, is a
contraction for INcoming SOLar radiATION.
Insolation depends on the zenith angle and the variable distance of
the earth from the sun.
The insolation integrated with time over the hours of daylight will give
the energy per unit area per day received at a point on the earth.

41. Example: On a clear day, measurements of the direct solar flux density F at
the earth’s surface in a wavelength interval give the following values:
Zenith angle (degree)
F ( )
Find 1) the solar flux density at the top of the atmosphere, and
2) the transmissivity of the atmosphere for normal incidence in this
wavelength interval.

42. 5. Atmospheric absorption and scattering of solar radiation
Solar radiation is essentially parallel beam radiation, i.e., all the radiation
is coming in from an infinitely small solid angle. For such radiation we
can use irradiance instead of radiance.
* Scattering
Rayleigh scattering:
For a scatter of a given size, the scattered intensity is
inversely proportional to the fourth power of wavelength.
Shorter wavelengths are scattered much more efficiently than
longer wavelengths.

43. 6. Solar heating rates
The absorption of solar radiation results in the heating
of the atmosphere.
The heating rate is proportional to the amount of energy
absorbed.

44. 8.5 Infrared radiation (Longwave radiation)
1. Infrared spectrum
* As the sun emits radiation over
all wavelengths, the earth and
the atmosphere also emit
radiation, which is referred to
as (thermal) infrared radiation.
* Solar and infrared spectra are
separated into two spectral
ranges above and below ~5 ,
and the overlap between them
is relatively small.

45. * The emitted Planck radiance from the earth and the atmosphere
is smaller than that of solar radiation, but the wavelength for the
intensity peak is longer.
* The equilibrium temperature of the earth-atmosphere system
Solar Spectrum
Infrared Spectrum

46. 2. Absorption of infrared radiation in the atmosphere
* The greenhouse effect (the atmospheric effect)
Energy emitted from the earth is absorbed by atmospheric
gases such as carbon dioxide, water vapor, ozone).
* The atmospheric window
The atmosphere is relatively transparent from wavelength
8 to , except for ozone which has an absorption
band in the region.

47. Atmospheric absorbers in the IR region:
* Ozone (consists of three oxygen atoms)
Is a very strong absorber in the UV, has rotational and vibrational transitions,
and absorbs strongly in the IR centered on the wavelength near
* Carbon dioxide (a linear molecule)
Has no permanent electric dipole, but as it vibrates a dipole can be
generated. Thus, it has vibrational bands, which are very important
for the atmosphere. Major bands are centered at and
* Water vapor (a bent molecule)
has strong absorption in many
bands throughout the IR region, and is
a strong absorber in the microwave
region.
* Nitrous oxide, methane, and
carbon monoxide
have two very strong
absorption bands in the IR.
has one strong band in the IR.

48. 3. Emission and infrared radiative transfer equation
A pencil of infrared radiation traversing an absorbing and
emitting medium will be weakened by the absorption, but it
may be strengthened by thermal emission from the medium.
This pencil of radiation is usually represented by its radiance
(or intensity) .
For downward propagating radiation:
For upward propagating radiation:

49. Example: Find the radiation temperature of the earth for a
solar constant of and an albedo of 30%.
If the albedo increased, would the radiation temperature
increase or decrease?
If the solar constant increased, would the radiation
temperature increase or decrease?

50. 4. Infrared cooling rates
Because the atmosphere loses radiative energy to space
through thermal infrared emission, it is normally cooled
by this process.

51. Infrared radiation between cloud and surface

52. 8.6 Radiation budgets
1. Radiation budget at the top of the atmosphere (TOA)
Gains of radiative
energy in the tropics
and subtropics
Losses in the polar
regions

53. 2. Radiation budget at the surface

54. 3. Radiative heating/cooling rates of the atmosphere
Atmospheric solar heating
is mainly produced by the
absorption of water vapor
in the troposphere and of
ozone in the stratosphere.

55. In general, IR radiation
serves to cool the atmosphere,
radiating away to space an
amount of energy equivalent
to the solar input, maintaining
the radiative balance.

56. Radiative cooling dominates
solar heating almost everywhere.
The ubiquitous net radiative
cooling in the earth’s
atmosphere is compensated for
by other forms of energy in the
atmosphere and by the
transport of heat from the
surface.

58. 4. Radiative equilibrium
Equilibrium temperature vs Surface temperature

59. Example: Assume that the atmosphere acts as a single
isothermal layer with a temperature that transmits
solar radiation but absorbs all thermal infrared radiation.
Show that the global surface temperature
Let the global albedo be 30%, and the solar content be
What is the global surface temperature?

60. 5. Radiative-convective equilibrium

61. 6. Radiation in energy balance climate model