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

n How much energy is emitted by some medium? n What “kind” of energy (what frequency/wavelength) is emitted by some medium? n What happens to radiation (energy) as it travels from the “target” (e.g., ground, cloud...) to the satellite’s sensor?

Frequency and wavelength v = c  Frequency (Hz) Wavelength Speed of light 1 hertz (Hz) = one cycle per second c = 3.0 x 10 8 ms -1

Electromagnetic spectrum  m1m1m1000  m 1m1000m 1,000,000  m = 1m GammaX rays Ultraviolet (UV) Infrared (IR)MicrowaveRadio waves Red (0.7  m) Orange (0.6  m) Yellow Green (0.5  m) Blue Violet (0.4  m) Visible Longer waves Shorter waves

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

Measuring energy n Radiant energy: Total energy emitted in all directions (J) n Radiant flux: Total energy radiated in all directions per unit time (W = J/s) n Irradiance (radiant flux density): Total energy radiated onto (or from) a unit area in a unit time (W m -2 ) n Radiance: Irradiance within a given angle of observation (W m -2 sr -1 ) Spectral radiance: Radiance for range in Spectral radiance: Radiance for range in

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

Electromagnetic radiation n Two fields: Electrical & magneticElectrical & magnetic n Travel perpendicular & speed of light n Property & behaves in predictable way n Frequency & wavelength n Photons/quanta C=3*10 8 =v *

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

Planck’s Function n Blackbody doesn't emit equal amounts of radiation at all wavelengths n Most of the energy is radiated within a relatively narrow band of wavelengths. n The exact amount of energy emitted at a particular wavelength lambda is given by the Planck function:

Planck’s function B (T) = c 1 -5 exp (c 2 / T ) -1 Irridance: Blackbody radiative flux for a single wavelength at temperature T (W m -2 ) Second radiation constant Absolute temperature First radiation constantWavelength of radiation Total amount of radiation emitted by a blackbody is a function of its temperature c 1 = 3.74x W m -2 c 2 = 1.44x10 -2 m °K

Planck curve

Wein’s Displacement Law m T =  m K Gives the wavelength of the maximum emission of a blackbody, which is inversely proportional to its temperature 300K: ~10  m 6000K: ~0.5  m

Intensity and Wavelength of Emitted Radiation : Earth and Sun

Rayleigh-Jeans Approximation B (T) = (c 1 / c 2 )  -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 T 4 (c 1 / c 2 )  -4 Brightness temperature (T B ) 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. B (T) T B =

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 temperatureradiatedblack body    absorbed /   incident  Absorptivity (r, reflectivity; t, transmissivity)

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

Solar Constant n The intensity of radiation from the Sun received at the top of the atmosphere n Changes in solar constant may result in climatic variations n solar-cycle-24.html

Solar Constant n While there are minor variations in solar output… n the amount of solar radiation at the top of the Earth’s atmosphere is fairly constant ~1367 W/m 2. n Its called the solar constant

The wavelengths we are most interested in for climatology and meteorology are between 0.01 and 100 μ m The wavelengths we are most interested in for climatology and meteorology are between 0.01 and 100 μ m

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

Processes: transmissionreflectionscatteringabsorptionrefractiondispersiondiffraction

transmission n the passage of electromagnetic radiation through a medium n transmission is a part of every optical phenomena (otherwise, the phenomena would never have occurred in the first place!)

reflection n 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.

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

Scattering n 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.

Molecular scattering (or other particles)

Scattering from irregular surface

Absorption (attenuation) n The process in which incident radiant energy is retained by a substance. A further process always results from absorption: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.

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

Refraction n The process in which the direction of energy propagation is changed as a result of: A change in density within the propagation medium, orA change in density within the propagation medium, or As energy passes through the interface representing a density discontinuity between two media.As energy passes through the interface representing a density discontinuity between two media.

Refraction in two different media less dense medium more dense medium

Refraction in two different media less dense medium more dense medium tt tt

Gradually changing medium ray wave fronts low density high density

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

The “classic” example white light prism

Diffraction n 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.

light Solid object shadow region

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

Optical phenomena process + atmospheric constituent optical phenomena atmospheric structure light

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

Optical phenomena process + atmospheric constituent optical phenomena atmospheric structure light

White clouds n scattering off cloud droplets ~ 20 microns

Dark clouds n scattering and attenuation from larger cloud droplets and raindrops

Blue skies n scattering from O 2 and N 2 molecules, dust violet light is scattered 16 times more than redviolet light is scattered 16 times more than red

Molecular scattering (nitrogen and oxygen) [blue scatters more than red]

Hazy (milky white) sky n Scattering from tiny particles terpenes (hydrocarbons) and ozoneterpenes (hydrocarbons) and ozone

Orange sun (as at sunset or sunrise) n Scattering from molecules This is the normal sunset we see frequentlyThis is the normal sunset we see frequently

Red sun (as at sunset or sunrise) n Scattering from molecules, dust, salt particles, volcanic material At 4° elevation angle, sun light passes through 12 times as much atmosphere as when directly overheadAt 4° elevation angle, sun light passes through 12 times as much atmosphere as when directly overhead

Green or blue sun n Scattering from volcanic ash, dust, smoke uniform-sized particlesuniform-sized particles

Twinkling (scintillation) n Refraction by small-scale temperature and relative humidity fluctuations

Twilight n Scattering and refraction by molecules and refractive index changes (air density decreases with altitude)

Back to remote sensing...

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

Atmospheric windows n Atmospheric window: An electromagnetic region where the atmosphere has little absorption and high transmittance n Absorption channel: An electromagnetic region where the atmosphere has high absorption n Atmospheric windows: Visible and Near IR wavelengthsVisible and Near IR wavelengths 3.7 and  m (IR) ; 2-4 and > 6 mm (MW)3.7 and  m (IR) ; 2-4 and > 6 mm (MW)

Atmospheric windows n Atmospheric windows are useful for gathering information about the surface of the Earth and clouds n Absorption channels are useful for gathering information about atmospheric properties Water vapor: 6.3  m channel on GOES satellitesWater vapor: 6.3  m channel on GOES satellites

Where are the windows?

n 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 Windows for Space-based Remote Sensing

Size parameter Type of scattering depends on size parameter (  ) Type of scattering depends on size parameter (  ) Size parameter compares radiation wavelength to size of scattering particlesSize parameter compares radiation wavelength to size of scattering particles Mie scattering for 0.1 <  < 50 (radiation and scattering particles are about same size) Mie scattering for 0.1 <  < 50 (radiation and scattering particles are about same size) Rayleigh scattering for  < 0.1 (scattering particles << than radiation) Rayleigh scattering for  < 0.1 (scattering particles << than radiation) Geometric optics for  > 50 (scattering particles >> than radiation) Geometric optics for  > 50 (scattering particles >> than radiation)  = 2r2r Radius of scattering particles

Size parameter  =  =  = 1  = 50 No scattering Rayleigh Mie Geometric (  m) r (  m)

Mie scattering  s ( ) =   r 2 Q s N(r) dr Scattering coefficient (similar to k in Beer’s equation) Radius of scattering particles Scattering efficiency for each scatterer { Number density of scatterers Scattering efficiency depends on the type of scatterer Number density is number of scatterers for some unit volume with some range in sizes

Rayleigh scattering  s ( ) =  r 2 Q s N Number density (no concern for range in sizes) Q s can be solved explicitly, as a function of the size parameter

Beer’s Law n The rate of decrease in intensity of radiation as it passes through a medium is proportional to the intensity of radiation Extinction may be due to scattering or absorption (scattering, absorption coefficients)Extinction may be due to scattering or absorption (scattering, absorption coefficients) = exp (-  x) II IoIo Initial flux density Flux density after passing medium Extinction coefficientDistance in medium

Beer’s Law for Air n Must add density into equation = exp (-  x) II IoIo Initial flux density Flux density after passing medium Extinction coefficientDistance in medium Density

Beer’s Law: A more general form n Absorption corss section gives the “shadow” cast by each particles = exp (-n b x) II IoIo Initial flux density Flux density after passing medium Number of particles per sq. m (m -2 ) Distance in medium Absorption cross section (m 2 )

Inverse Squared Law n Radiation from a spherical source (e.g., Sun) decreases with the square of the distance E 2 = E 1 (R 1 / R 2 ) 2 Final flux density Radius of emitter (e.g., Sun) Distance of target from emitter (e.g., distance of Earth from Sun) Initial flux density