11

Microwave Interactions with Microwave Interactions with the Atmospherethe Atmosphere

S. L. Cruz PolS. L. Cruz PolElectrical and Computer EngineeringElectrical and Computer Engineering

University of Puerto RicoUniversity of Puerto Rico

22

Atmosphere compositionAtmosphere composition

Typical Atmosphere in %

78

210.93

Ni

O2

Ar

Other components:

Carbon dioxide (CO2), Neon (Ne), Helium (He), Methane (CH4), Krypton (Kr), Hydrogen (H2) and Water vapor (highly variable)

33

Atmospheric ConstituentsAtmospheric Constituents

44

IntroductionIntroduction

Up to now, we have assumed lossless atm.Up to now, we have assumed lossless atm. For For 1 GHz< f< 15 GHz1 GHz< f< 15 GHz ~lossless ~lossless For higher frequencies, =>absorption bandsFor higher frequencies, =>absorption bands

H2O O2

•22.235 GHz•183.3 GHz•IR & visible

•50-70GHz•118.7GHz•IR & visible

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OutlineOutline

I. The atmosphere: composition, profileI. The atmosphere: composition, profileII. Gases: many moleculesII. Gases: many molecules

1. 1. ShapesShapes((G, VVW, LG, VVW, L): ): below 100GHz, up to 300GHzbelow 100GHz, up to 300GHz

e.g.e.g. HH22O , OO , O22

2. 2. Total AtmosphericTotal Atmospheric Absorption Absorption gg, , opacity opacity , , and atm-lossesand atm-losses L L

3. 3. TTBB: : Downwelling Emission by AtmosphereDownwelling Emission by Atmosphere

Sky Temp= cosmic + galaxySky Temp= cosmic + galaxy

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U.S. Standard AtmosphereU.S. Standard Atmosphere

Troposphere – clouds, weather

Stratosphere- no H2O or dustozone absorption of UV warms air to ~40oF

Mesosphereno aircrafts heretoo cold ~-90oF

Thermosphere(or Ionosphere) 1000-3000oF!

Tropopause

Stratopause

Mesopause

10km

P= 1013 mbars = 1013 HPaT= 300K

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Atmospheric ProfilesAtmospheric ProfilesUS Standard Atmosphere 1962US Standard Atmosphere 1962

TemperatureTemperature

DensityDensity

Pressure Pressure P= P= nRT/V=nRT/V=airairRT/M or PRT/M or Pooee-z/H-z/H33

height scale Pressure 7.7 where 3 kmH

km 320km2 )20(

km 20km 11 km 110

)(

)11(

)11(

zzTzTzazT

zTo

1/225.1)( Hzair ez

)]3.7/sin(3.01[225.1)( 3.7/ zez zair or

height scaledensity 5.9 where 1 kmH

88

Water Vapor ProfileWater Vapor Profile

Depends on factors like weather, seasons, time of the day.It’s a function of air temperature.•Cold air can’t hold water•Hot air can support higher humidities.(P dependence)

v(z)oe-z/H4 [g/m3]where o averages 7.72 in mid latitudesand the total mass of water vapor in a column of unit cross section is

40

)( HdzzM o

height scalevapor - water5.22between where 4 kmH

99

1010

EM interaction with MoleculesEM interaction with Molecules Total internal energy state for a moleculeTotal internal energy state for a molecule

– electronicelectronic energy corresponding to atomic level energy corresponding to atomic level– vibrationvibration of atoms about their equilibrium position of atoms about their equilibrium position – rotationrotation of atoms about center of molecule of atoms about center of molecule – EE = = EEee + + EEvv + + EErr

Bohr conditionBohr condition ffmlml= (= (EEmm - - EEll ) /h ) /h Values for energy differences forValues for energy differences for

– electronicelectronic: : 22 to to 1010 eV eV– vibrational-rotationalvibrational-rotational: : 0.10.1 to to 22 eV eV– pure rotationalpure rotational: : 1010-4-4 to to 5 x 105 x 10-2-2 eV ( eV ( microwavesmicrowaves))

1111

Line ShapesLine Shapes

where,where,– SSlmlm is the line strength is the line strength

– F(f,fF(f,flmlm)) is the line shape is the line shape

LINE SHAPESLINE SHAPES– LorentzLorentz– GrossGross– Van-Vleck-WeisskoptVan-Vleck-Weisskopt

Abs

orpt

ion

),(4),( lmlmlma ffFScfff

frequency

frequency

One molecule

Many molecules:pressure broaden*

*caused by collision between molecules

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Line shapesLine shapes

LorentzLorentz

GrossGross

Van-Vleck-WeisskoptVan-Vleck-Weisskopt

22)(1),(

lmlmL ff

ffF

22222 4)(41),(

fffffffF

lm

lmlmG

2222

2

)()(1),(

ffffffffF

lmlmlmlmvw

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Absorption BandsAbsorption Bands Mainly water and oxygen for microwavesMainly water and oxygen for microwaves

Brig

htne

ss T

empe

ratu

re [K

]B

right

ness

Tem

pera

ture

[K]

Frequency [GHz]Frequency [GHz]

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Total AtmosphericTotal Atmospheric

AbsorptionAbsorptiongg, ,

Opacity Opacity , ,

Loss factorLoss factor L L

22 OOHg

o

e dzz

sec

sec)(0

0sec)(

secdzzg

o eeL

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Atmospheric EmissionAtmospheric Emission For clear atmosphereFor clear atmosphere

wherewhere

Also there is some background radiationAlso there is some background radiation

TTcoscos=2.7K from the Big Bang and =2.7K from the Big Bang and TTgalgal~0 above 5GHz~0 above 5GHz

0

sec)',0( ')'()'(sec dzezTzT zaDN

0

)()',0( dzzz a

gallacticmicextra TTT cos

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Relative HumidityRelative Humidity

Air Air TemperatureTemperature

Vapor air can Vapor air can holdhold

Actual Vapor in Actual Vapor in the airthe air

[gr per kg dry air][gr per kg dry air]

Relative Relative humidityhumidity

8686ooFF 27.627.6 10.8310.83 39%39%

7777ooFF 20.420.4 10.8310.83 53%53%

6868ooFF 14.914.9 10.8310.83 72%72%

5959ooFF 10.810.8 10.8310.83 100%100%

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AvirisAviris