1. Meteorology ENV 2A23
Radiation Lectures

2. How is energy transferred?

3. How is energy transferred?

5. Conduction
Convection
Radiation

6. Conduction
Convection
Radiation

7. Conduction
Convection
Radiation

8. How is energy transferred?
Conduction – energy transfer from molecule to molecule
Convection – spatial mixing of “air parcels” i.e. masses of air
Radiation – primary source of energy for the Earth
Radiation imbalances drive the circulation of the atmosphere and ocean

9. Electomagnetic radiation in the range 0.1 to 10 micrometres (mm), i.e. 0.1-10 x10-6 m

10. Electomagnetic radiation travels in packets (quanta), whose energy is given by
E = hc/8,
where 8 is wavelength,
h is Planck’s constant (6.625x10-34 J s-1)
c is speed of light (3x108 m s-1)

11. The Sun
Most solar radiation is emitted from the photosphere (T~6000 K)
Sun powered by nuclear fusion, H to He
Plasma ejected as “solar wind”

12. The Sun
The sun’s radiative output is centred on visible wavelengths

13. The Sun The sun’s output is not constant Sunspot cycle ~11 years
Periods of high/low activity

14. Sun-Earth Geometry Axial tilt = 23.5o Eccentricty = 0.02
Aphelion = 1.50x108 km, 3 July
Perihelion = 1.45x108 km, 3 January
SH receives more solar radiation in summer than NH
Is it warmer?

15. Sun-Earth Geometry
Equinoxes = “equal” days and nights

16. Sun-Earth Geometry
Solstice = “sun stands still”, longest/shortest days

17. Changes in orbital parameters result in changes in incoming solar radiation and distribution (Milankovitch 1930)
Orbital feature
Range
Period
(years)
Radiation changes
Tilt
21.8o to 24.4o
40,000
Seasonal radiation balance only
Eccentricity
0 to 0.06
96,000
Seasonal balance and total radiation by ±15%
Precession of equinoxes
orbit
21,000
Seasonal affects

18. The Sun’s energy output
The solar constant is the radiation flux density at the top of the atmosphere, for the mean sun-earth distance
i.e. the amount of radiation falling on the top of the atmosphere (per unit area)
S0 = 1360 W m-2

19. The Sun’s energy output
The sun is an almost perfect emitter of radiation, i.e. emits maximum possible radiation for its temperature
It is a blackbody emitter and so governed by Stephan-Boltzmann Law:
F = FT4, where, F is flux density W m-2,
T is temperature,
F = 5.67x10-8 W m-2 K-4

20. Radiation flux density at the Earth
sun rs rd
earth
F = FT4 per unit area
So over sphere 4Brs2FT4
Hence at distance of earth (rd): 4Brs2FT4/ 4Brd2
i.e. S0 = rs2/rd2 FT4, an inverse square law

21. Emission temperature of a planet
The emission temperature of a planet is the blackbody temperature with which it needs to emit radiation in order to achieve energy balance. To calculate this for the Earth, equate blackbody emission with amount of solar energy absorbed.
- see radiation practical

22. Emission temperature of a planet
Energy incident on planet = solar flux density x shadow area
But not all radiation is absorbed, some is reflected:
albedo (α) = reflected/incident radiation
Absorbed solar radiation = S0(1- α)π re2 (W)
Absorbed solar radiation per unit area = S0(1- α)/4 (W m-2)
This must be balanced by terrestrial emission.
If we approximated Fe as a blackbody:
FEarth = σTe4 , where Te is the blackbody emission temperature.
=> Te4 = S0(1- α)/σ4
For Earth, Te = 255 K.
Note this is well below the average surface air temperature of the Earth = 288 K.

23. Distribution of Insolation
Seasonal & latitudinal variations in temperature are driven primarily by variations in insolation
The amount of solar radiation incident on the top of the atmosphere depends on:

24. Distribution of Insolation
Seasonal & latitudinal variations in temperature are driven primarily by variations in insolation
The amount of solar radiation incident on the top of the atmosphere depends on:
Latitude
Season
Time of day

25. Distribution of Insolation
The solar zenith angle (2s) is the angle between the local normal to the Earth’s surface & the line between the Earth’s surface & the sun
The (daily) solar flux per unit area can be calculated as:
where S0 is the solar constant, and d is the sun-earth distance 2s
earth

26. Distribution of Insolation
The season ~ declination angle *,
i.e. latitude on Earth’s surface directly under the sun at noon
- * varies between 23.5 & -23.5o
The time of day ~ hour angle h,
Longitude of subsolar point relative to its position at noon
Then cos θs = sinφ sinδ + cosφ cosδ cosh, for latitude φ

27. Distribution of Insolation

28. Distribution of Insolation
Equator receives more solar radiation than the poles (at the top of the atmosphere)

29. Energy balance at the top of the atmosphere
As well as the distribution of insolation, the amount of energy absorbed and emitted depends on atmospheric and surface conditions.

30. Energy balance at the top of the atmosphere
albedo (α) = reflected/incident radiation

31. Energy balance at the top of the atmosphere
Outgoing longwave radiation

32. Energy balance at the top of the atmosphere
Net radiation
The net radiation can be calculated from
R = SWd – SWu + LWd – LWu ,
Where
SW = shortwave (solar) radiation,
LW = longwave (terrestrial radiation)
=> R = SWd(1-αp) –LWu
at the top of the atmosphere,
where αp is the planetary albedo.

33. Energy balance at the top of the atmosphere
=> R = SWd(1-αp) –LWu
at the top of the atmosphere,
where αp is the planetary albedo.

34. Energy balance at the top of the atmosphere
There must be a poleward transport of energy to balance out the net gain at the equator and the net loss at the poles.

35. Radiation Flux and Radiation Intensity
The radiation flux density (or irradiance), F (units W m-2) is the radiant energy crossing a unit area in unit time. It does not discriminate between different directions.
The radiation intensity (or radiance), I, (units W m-2 steradians-1) includes information on directionality.
Special Case :
Radiation intensity I is isotropic,
Then F = BI
For example: emission from a blackbody, emission from the atmosphere
Animation…

36. What about the wavelength of the radiation?
Planck’s Law
i.e. B Bv(T) dv = FT4
In other words, radiation intensity depends on frequency (or equivalently wavelength) of emission.

37. What about the wavelength of the radiation?
Wein’s Law
Sun’s emission peaks ~ 4.8 microm
Earth’s emission peaks ~ 10 microm
Brightness temperatures of the sun and Earth are ~6000 K and 255 K

38. What about the wavelength of the radiation?
When an object is not a blackbody, then its radiation flux density can be written
F = eσT4, where e is the emissivity.
Usually eλ = e(λ) is a function of wavelength.
If we define absorptivity aλ as the fraction of incident radiation that is absorbed. It can be shown that
eλ = aλ , this is Kirchoff’s Law.
i.e. an object emits radiation at each wavelength as efficiently as it absorbs it.

39. Radiation in the atmosphere
Earlier we found the blackbody emission temperature Te = 255 K, much colder than the observed Tsurface = 288 K.
Why ?

40. Radiation in the atmosphere
Difference is due to selective scattering, absorption and emission of radiation by the atmosphere.
These depend upon the structure of the molecules present.
sketch

41. Radiation in the atmosphere
Difference is due to selective scattering, absorption and emission of radiation by the atmosphere.
These depend upon the structure of the molecules present.

42. Scattering Scattering decreases the intensity of the solar beam.
It depends upon λ (wavelength) and d (particle size).
Three cases:

43. (1) Rayleigh Scattering occurs when d << λ
For example from O2 or N2, the major tropospheric gases, where d = m and λ = 0.5x10-6 m.
Scatters equal amounts of radiation forward and backward
The amount of scattering strongly dependent on λ:
the volume extinction coefficient is a function of 1/ λ4
Rayleigh scattering explains why the sky is blue and sunsets are red.
- blue (short λ) scattered more than red (long λ) light

44. (2) Diffuse scattering occurs when d >> λ
Diffuse scattering occurs when d >> λ, for example from dust or cloud droplets
Typically ~10 mm
Diffuse scattering is independent of λ.
Clouds appear white and polluted skies are pale
Full consideration requires Mie theory.

45. (3) Complex Scattering occurs when d = λ
Diffraction

46. Absorption
All gases absorb and re-radiate energy at specific wavelengths depending on their molecular structure.
Electronic excitation – visible uv
Vibrational excitation – IR
Rotational excitation – thermal IR
Molecules need a permanent electric dipole, e.g. H2O O - H H +

48. Aborption occurs at specific wavelengths (lines) according to the excitational properties of the gas (or gases) involved.
However these lines are broadened by various mechanisms into absorption bands.

49. Absorption line broadening
Natural broadening – associated with the finite time of photon emission and the uncertainty principle
Pressure broadening (or collision broadening) – collisions between molecules supply or remove small amounts of energy during radiative transitions.
- Primary mechanism in the troposphere (why?)
Doppler broadening – results from the movement of molecules relative to photons.
- dominant at higher altitudes

50. Groups of lines within a frequency interval are termed absorption bands
In the thermal infra-red there are important absorption bands due to H2O, CO2, O3, CH4, N2O, etc

51. Bottom panel shows atmosphere is generally opaque to IR radiation
There are important “windows” at 8-9 mm and mm.
It is through these “windows” that most passive satellite sensors observe radiation emissions

52. For example, this geostationary Meteosat image shows radiation emitted in the IR at 10.5-12.5 mm.

53. Clouds and radiation
Clouds consist of liquid water droplets or ice particles suspended in the atmosphere
The droplets or ice particles interact with both solar and terrestrial (IR) radiation, depending on their size and shape.

58. i.e. the cloud albedo is a function of total liquid water content and solar zenith angle.

59. Thick clouds (e.g. 1 km), e.g. cumulus, a = 0.9
Thin clouds (e.g. 100 m), e.g. stratus, a = 0.7
Very important for planetary albedo

60. Global (1 dimensional) Energy Balance
Observations from the ground & space of emitted radiation, combined with climatological surface energy flux observations have allowed an average (1D) picture of energy transfer through the Earth’s atmosphere to be estimated.

61. SH = sensible heat fluxes, LE = latent heat fluxes

62. Solar: 100 units incoming, 70 absorbed, 30 reflected or scattered
Terrestrial 110 emitted from surface!
The strong downward LW emission (89) is responsible for modulating the diurnal cycle

63. Further reading:
Chapters 2 and 3 Ahrens