Electromagnetic Spectrum and Laws of Radiation

1. Electromagnetic Spectrum and Laws of Radiation Satellite Meteorology/Climatology Professor Menglin Jin

2. 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?

3. Frequency and wavelength Speed of light c v = Frequency (Hz)  Wavelength 1 hertz (Hz) = one cycle per second c = 3.0 x 108 ms-1

4. Electromagnetic spectrum Red (0.7m) Orange (0.6m) Yellow Green (0.5m) Blue Violet (0.4m) Visible Ultraviolet (UV) Radio waves Microwave Infrared (IR) X rays Gamma 1000m 1m 1000 m 1m 0.001m Longer waves Shorter waves 1,000,000m = 1m

5. Blackbody radiation • Examine relationships between temperature, wavelength and energy emitted • Blackbody: A “perfect” emitter and absorber of radiation... does not exist

6. Measuring energy • 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 

7. Radiance Toward satellite Normal to surface Solid angle, measured in steradians (1 sphere = 4 sr = 12.57 sr)

8. Electromagnetic radiation • Two fields: • Electrical & magnetic • Travel perpendicular & speed of light • Property & behaves in predictable way • Frequency & wavelength • Photons/quanta C=3*108=v * 

9. Stefan-Boltzmann Law M BB = T 4 Total irradiance emitted by a blackbody (sometimes indicated as E*) Stefan-Boltzmann constant 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

10. 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:

11. 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

12. Planck curve

13. 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

14. Intensity and Wavelength of Emitted Radiation : Earth and Sun

15. 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.

16. 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)

17. Kirchoff’s Law Materials which are strong absorber at a particular wavelength are also strong emitter at that wavelength

18. Solar Constant • The intensity of radiation from the Sun received at the top of the atmosphere • Changes in solar constant may result in climatic variations • http://www.space.com/scienceastronomy/071217-solar-cycle-24.html

19. Solar Constant • While there are minor variations in solar output… • the amount of solar radiation at the top of the Earth’s atmosphere is fairly constant ~1367 W/m2. • Its called the solar constant

20. The wavelengths we are most interested in for climatology and meteorology are between 0.01 and 100 μm

21. Radiative Transfer What happens to radiation (energy) as it travels from the “target” (e.g., ground, cloud...) to the satellite’s sensor?

22. Processes: transmission reflection scattering absorption refraction dispersion diffraction

23. 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!)

24. reflection • 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.

25. Reflection from smooth surface light ray angle of reflection angle of incidence

26. Scattering • 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.

27. Molecular scattering (or other particles)

28. Scattering from irregular surface

29. Absorption (attenuation) • 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.

30. incident radiation substance (air, water, ice, smog, etc.) transmitted radiation absorption

31. Refraction • 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.

32. Refraction in two different media less dense medium more dense medium

33. Gradually changing medium low density ray wave fronts high density

34. Dispersion • the process in which radiation is separated into its component wavelengths (colors).

35. The “classic” example white light prism

36. Diffraction • 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.

37. light shadow region Solid object

38. Atmospheric Constituents: empty space molecules dust and pollutants salt particles volcanic materials cloud droplets rain drops ice crystals

39. Optical phenomena light atmospheric constituent optical phenomena + process atmospheric structure

40. Atmospheric Structure temperature gradient humidity gradient clouds layers of stuff- pollutants, clouds

41. Remote sensing system Applications A technology used for obtaining information about a target through the analysis of data acquired from the target at a distance.

42. Atmospheric windows • 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)

43. 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 • Water vapor: 6.3m channel on GOES satellites

44. Where are the windows?

45. Windows for Space-based Remote Sensing • 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

46. Size parameter • Type of scattering depends on size parameter () • Size parameter compares radiation wavelength to size of scattering particles • Mie scatteringfor 0.1 <  < 50 (radiation and scattering particles are about same size) • Rayleigh scatteringfor  < 0.1 (scattering particles << than radiation) • Geometric opticsfor  > 50 (scattering particles >> than radiation) 2r Radius of scattering particles  = 

47. Size parameter Geometric  = 50  = 1  = 10-1 Mie r (m)  = 10-3 Rayleigh No scattering  (m)

48. 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 efficiencydepends on the type of scatterer Number densityis number of scatterers for some unit volume with some range in sizes

49. 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