Electromagnetic Spectrum and Laws of Radiation

Satellite Satellite Meteorology/ClimatologyMeteorology/Climatology

Professor Menglin JinProfessor Menglin Jin

How much energy is emitted by some How much energy is emitted by some medium? medium?

What “kind” of energy (what What “kind” of energy (what frequency/wavelength) is emitted by frequency/wavelength) is emitted by some medium?some medium?

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

Frequency and wavelength

v = c

Frequency (Hz)

Wavelength

Speed of light

1 hertz (Hz) = one cycle per secondc = 3.0 x 108 ms-1

Electromagnetic spectrum

0.001m1m1000 m1m1000m

1,000,000 m = 1m

GammaX raysUlt

ravi

olet

(U

V)

Infrared (IR)MicrowaveRadio waves

Red(0.7m)

Orange(0.6m)

YellowGreen

(0.5m)Blue

Violet(0.4m)

Visible

Longer waves Shorter waves

Blackbody radiation

Examine relationships between Examine relationships between temperature, wavelength and temperature, wavelength and energy emittedenergy emitted

Blackbody: A “perfect” emitter and Blackbody: A “perfect” emitter and absorber of radiation... does not absorber of radiation... does not existexist

Measuring energy

Radiant energy: Total energy emitted in Radiant energy: Total energy emitted in all directions (J)all directions (J)

Radiant flux: Total energy radiated in all Radiant flux: Total energy radiated in all directions per unit time (W = J/s)directions per unit time (W = J/s)

Irradiance (radiant flux density): Total Irradiance (radiant flux density): Total energy radiated onto (or from) a unit energy radiated onto (or from) a unit area in a unit time (W marea in a unit time (W m-2-2))

Radiance: Irradiance within a given Radiance: Irradiance within a given angle of observation (W mangle of observation (W m-2-2 sr sr-1-1))

Spectral radiance: Radiance for range in Spectral radiance: Radiance for range in

Radiance

Toward satellite

Solid angle, measured in steradians(1 sphere = 4 sr = 12.57 sr)

Normalto surface

Electromagnetic radiation Two fields:Two fields:

• Electrical & Electrical & magneticmagnetic

Travel Travel perpendicular & perpendicular & speed of lightspeed of light

Property & Property & behaves in behaves in predictable waypredictable way

Frequency & Frequency & wavelengthwavelength

Photons/quantaPhotons/quantaC=3*108=v *

Stefan-Boltzmann Law

M BB = T 4

Total irradianceemitted 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

Blackbody doesn't emit equal amounts Blackbody doesn't emit equal amounts of radiation at all wavelengthsof radiation at all wavelengths

Most of the energy is radiated within a Most of the energy is radiated within a relatively narrow band of wavelengths. relatively narrow band of wavelengths.

The exact amount of energy emitted at The exact amount of energy emitted at a particular wavelength a particular wavelength lambdalambda is given is given by the Planck function:by the Planck function:

Planck’s function

B (T) = c1-5

exp (c2 / T ) -1

Irridance:Blackbody radiative fluxfor a single wavelength at temperature T (W m-2)

Second radiation constantAbsolute temperature

First radiation constant Wavelength of radiation

Total amount of radiation emitted by a blackbody is a function of its temperaturec1 = 3.74x10-16 W m-2 c2 = 1.44x10-2 m °K

Planck curve

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 mSun @ 6000K: ~0.5 m

Intensity and Wavelength of Emitted Radiation : Earth and Sun

Rayleigh-Jeans Approximation

B (T) = (c1 / c2) -4 T

When is this valid: 1. For temperatures encountered on Earth 2. For millimeter and centimeter wavelengthsAt microwave wavelengths, the amount of radiation emitted is directly proportional to T... not T4

(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.

B (T)TB =

Emissivity and Kirchoff’s Law

Actual irradiance bya non-blackbodyat 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

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

The intensity of radiation from the Sun The intensity of radiation from the Sun received at the top of the atmospherereceived at the top of the atmosphere

Changes in solar constant may result in Changes in solar constant may result in climatic variationsclimatic variations

http://www.space.com/http://www.space.com/scienceastronomy/071217-solar-cycle-scienceastronomy/071217-solar-cycle-24.html24.html

Solar Constant While there are minor While there are minor

variations in solar variations in solar output…output…

the amount of solar the amount of solar radiation at the top of radiation at the top of the Earth’s atmosphere the Earth’s atmosphere is fairly constant ~1367 is fairly constant ~1367 W/mW/m22..

Its called the Its called the solar solar constantconstant

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

Radiative Transfer

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

Processes:

transmissiontransmissionreflectionreflectionscatteringscatteringabsorptionabsorptionrefractionrefractiondispersiondispersiondiffractiondiffraction

transmission

the passage of electromagnetic the passage of electromagnetic radiation through a mediumradiation through a medium

transmission is a part of transmission is a part of everyevery optical phenomena (otherwise, the optical phenomena (otherwise, the phenomena would never have phenomena would never have occurred in the first place!)occurred in the first place!)

reflection

the process whereby a surface of the process whereby a surface of discontinuity turns back a portion discontinuity turns back a portion of the incident radiation into the of the incident radiation into the medium through which the medium through which the radiation approached; the reflected radiation approached; the reflected radiation is at the same angle as radiation is at the same angle as the incident radiation.the incident radiation.

Reflection from smooth surface

angle of incidence

angle ofreflection

light ray

Scattering

The process by which small The process by which small particles suspended in a medium particles suspended in a medium of a different index of refraction of a different index of refraction diffusediffuse a portion of the incident a portion of the incident radiation in radiation in allall directions. No directions. No energy transformation results, only energy transformation results, only a change in the spatial distribution a change in the spatial distribution of the radiation.of the radiation.

Molecular scattering (or other particles)

Scattering from irregular surface

Absorption (attenuation)

The process in which incident The process in which incident radiant energy is retained by a radiant energy is retained by a substance. substance. • A further process always results from A further process always results from

absorption:absorption:– The irreversible conversion of the The irreversible conversion of the

absorbed radiation goes into some other absorbed radiation goes into some other form of energy (usually heat) within the form of energy (usually heat) within the absorbing medium.absorbing medium.

substance (air, water, ice, smog, etc.)

incidentradiation

absorption

transmittedradiation

Refraction

The process in which the The process in which the direction direction of energy propagation is of energy propagation is changedchanged as a result of: as a result of: • A change in density within the A change in density within the

propagation medium, orpropagation medium, or• As energy passes through the As energy passes through the

interface representing a density interface representing a density discontinuity between two media.discontinuity between two media.

Refraction in two different media

less densemedium

more densemedium

Gradually changing medium

ray

wavefronts

low density

high density

Dispersion

the process in which radiation is the process in which radiation is separated into its component separated into its component wavelengths (wavelengths (ccoolloorrss).).

The “classic” example

white light

prism

Diffraction

The process by which the direction The process by which the direction of radiation is changed so that it of radiation is changed so that it spreads into the geometric shadow spreads into the geometric shadow region of an opaque or refractive region of an opaque or refractive object that lies in a radiation field.object that lies in a radiation field.

light

Solid object

shadowregion

Atmospheric Constituents:

empty spaceempty spacemoleculesmoleculesdust and pollutantsdust and pollutantssalt particlessalt particlesvolcanic materialsvolcanic materialscloud dropletscloud dropletsrain dropsrain dropsice crystalsice crystals

Optical phenomena

process + atmosphericconstituent

opticalphenomena

atmosphericstructure

light

Atmospheric Structure

temperature gradienttemperature gradient

humidity gradienthumidity gradient

cloudsclouds

layers of layers of stuff - pollutants, clouds- pollutants, clouds

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

Atmospheric window: Atmospheric window: An electromagnetic An electromagnetic region where the atmosphere has little region where the atmosphere has little absorption and high transmittanceabsorption and high transmittance

Absorption channel: Absorption channel: An electromagnetic An electromagnetic region where the atmosphere has high region where the atmosphere has high absorptionabsorption

Atmospheric windows:Atmospheric windows:• Visible and Near IR wavelengthsVisible and Near IR wavelengths• 3.7 and 8.5-12.5 3.7 and 8.5-12.5 m (IR) ; 2-4 and > 6 mm m (IR) ; 2-4 and > 6 mm

(MW)(MW)

Atmospheric windows

Atmospheric windows are useful Atmospheric windows are useful for gathering information about the for gathering information about the surface of the Earth and cloudssurface of the Earth and clouds

Absorption channels are useful for Absorption channels are useful for gathering information about gathering information about atmospheric propertiesatmospheric properties• Water vapor: 6.3Water vapor: 6.3m channel on GOES m channel on GOES

satellitessatellites

Where are the windows?

Space-based remote sensors allow us to observe & quantify Space-based remote sensors allow us to observe & quantify Earth’s environments in regions of the electromagnetic Earth’s environments in regions of the electromagnetic spectrum to which our eyes are not sensitivespectrum 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 Size parameter compares radiation wavelength to size of

scattering particlesscattering particles Mie scatteringMie scattering for 0.1 < for 0.1 < < 50 (radiation and < 50 (radiation and

scattering particles are about same size)scattering particles are about same size) Rayleigh scatteringRayleigh scattering for for < 0.1 (scattering particles < 0.1 (scattering particles

<< than radiation)<< than radiation) Geometric opticsGeometric optics for for > 50 (scattering particles >> > 50 (scattering particles >>

than radiation)than radiation)

= 2r

Radius of scattering particles

Size parameter

1e-01 1e+00 1e+01 1e+02 1e+03 1e+04 1e+05 1e+061e-04

1e-03

1e-02

1e-01

1e+00

1e+01

1e+02

1e+03

1e+04

1e+05

= 10-3

= 10-1 = 1 = 50

No scattering

Rayleigh

Mie

Geometric

(m)

r (

m)

Mie scattering

s() = r2 Qs N(r) dr

Scattering coefficient(similar to k in Beer’s

equation)

Radius ofscattering particles

Scattering efficiencyfor each scatterer

{

Number density of scatterers

Scattering efficiency depends on the type of scattererNumber density is number of scatterers for some unit volume with some range in sizes

Rayleigh scattering

s() = r2 Qs N

Number density(no concern for range in sizes)

Qs can be solved explicitly, as a function ofthe size parameter

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Beer’s Law

The rate of decrease in intensity of radiation as it passes through a medium is The rate of decrease in intensity of radiation as it passes through a medium is proportional to the intensity of radiationproportional 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

Io

Initial flux density

Flux density after passing

medium

Extinction coefficient Distance in medium

Beer’s Law for Air

Must add density into equationMust add density into equation

= exp (-x)I

Io

Initial flux density

Flux density after passing

medium

Extinction coefficient Distance in medium

Density

Beer’s Law: A more general form

Absorption corss section gives the Absorption corss section gives the “shadow” cast by each particles“shadow” cast by each particles

= exp (-n b x)I

Io

Initial flux density

Flux density after passing

medium

Number of particlesper sq. m (m-2)

Distance in medium

Absorption cross section(m2)

Inverse Squared Law

Radiation from a spherical source Radiation from a spherical source (e.g., Sun) decreases with the (e.g., Sun) decreases with the square of the distancesquare of the distance

E2 = E1 (R1 / R2 )2 Final flux density

Radius of emitter(e.g., Sun)

Distance of target fromemitter (e.g., distanceof Earth from Sun)

Initial flux density