microwave interactions with the atmosphere
DESCRIPTION
Microwave Interactions with the Atmosphere. Dr. Sandra Cruz Pol Microwave Remote Sensing INEL 6669 Dept. of Electrical & Computer Engineering, UPRM, Mayagüez, PR. Atmosphere composition. Other components: - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/1.jpg)
Microwave Interactions with Microwave Interactions with the Atmospherethe Atmosphere
Dr. Sandra Cruz PolDr. Sandra Cruz PolMicrowave Remote Sensing INEL 6669Microwave Remote Sensing INEL 6669Dept. of Electrical & Computer Engineering,Dept. of Electrical & Computer Engineering,UPRM, Mayagüez, PRUPRM, Mayagüez, PR
![Page 2: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/2.jpg)
Atmosphere compositionAtmosphere compositionTypical 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)
![Page 3: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/3.jpg)
Air Constituents Air Constituents in Troposphere and in Troposphere and StratosphereStratosphere
NN22 78.1%, O 78.1%, O22 20.9%, H 20.9%, H22O 0-2%O 0-2%
Inert gases 0.938%Inert gases 0.938%
Many of the least abundant have a disproportionally large Many of the least abundant have a disproportionally large influence on atmospheric transmissioninfluence on atmospheric transmission..
COCO22 398ppm 398ppm absorbs 2.8, 4.3 & 15 absorbs 2.8, 4.3 & 15 mm
CHCH44 1.7ppm 1.7ppm absorbs 3.3 & 7.8absorbs 3.3 & 7.8mm
NN22O .35ppm O .35ppm absorbs 4.5, 7.8 & 17absorbs 4.5, 7.8 & 17mm
OO33 ~10 ~10-8-8 absorbs UV-B, 9.6absorbs UV-B, 9.6mm
CFClCFCl33, CF, CF22CLCL22 … … absorbs IRabsorbs IR
![Page 4: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/4.jpg)
Atm. COAtm. CO22 Concentration Concentration
Last 200 years
![Page 5: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/5.jpg)
![Page 6: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/6.jpg)
Methane
![Page 7: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/7.jpg)
![Page 8: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/8.jpg)
![Page 9: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/9.jpg)
HH22O is less than 2% yet has great O is less than 2% yet has great
effect in climate & weathereffect in climate & weather
![Page 10: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/10.jpg)
Radiative Transfer in AtmosphereRadiative Transfer in Atmosphereduring Daytimeduring Daytime
During daytime only. Nighttime is another story
![Page 11: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/11.jpg)
Atm. Gases & Electromagnetic Atm. Gases & Electromagnetic propagationpropagation
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
![Page 12: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/12.jpg)
OutlineOutline
I. The atmosphere: composition, profileI. The atmosphere: composition, profile
II. Gases: many moleculesII. Gases: many molecules1. 1. ShapesShapes((G, VVW, LG, VVW, L): ): below 100GHz, up to 300GHzbelow 100GHz, up to 300GHz
we find interaction with we find interaction with HH22O and OO and 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
![Page 13: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/13.jpg)
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
8/15km
P= 1013 mbars = 1013 HPaT= 300K
50/60km
95/120km
![Page 14: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/14.jpg)
Atmospheric ProfilesAtmospheric ProfilesUS Standard Atmosphere 1962US Standard Atmosphere 1962
TemperatureTemperature
Density in kg/mDensity in kg/m33
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(
zzT
zT
zazT
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
Rair= 2.87
![Page 15: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/15.jpg)
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 vaportotal mass of water vapor in a in a columncolumn of unit cross section is of unit cross section is
4
0
)( HdzzM o
height scalevapor - water5.22between where 4 kmH
![Page 16: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/16.jpg)
Relative HumidityRelative Humidity
Dew point Dew point temperature (dew=rocío)temperature (dew=rocío)– is the T below which the WV in a volume of humid is the T below which the WV in a volume of humid
air at a constant barometric P will condense into air at a constant barometric P will condense into liquid water.liquid water.
– Is the Is the TT as which as which fogfog forms forms
Relative HumidityRelative Humidity– When When TTairair is close to is close to TTdewdew => => high %RHhigh %RH
Absolute HumidityAbsolute Humidity, the mass of water per unit , the mass of water per unit volume of air. volume of air.
![Page 17: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/17.jpg)
Equations for RHEquations for RH
Where e = pressure and exp means exponential ex
![Page 18: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/18.jpg)
Relative Humidity (RH) Relative Humidity (RH) simplified equationssimplified equations
T is in Celsius
![Page 19: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/19.jpg)
Relative Humidity, RHRelative Humidity, RHvapor in airvapor in air
Air Air TemperatureTemperature
TT
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
RHRH
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%
![Page 20: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/20.jpg)
Relative Humidity, RHRelative Humidity, RHdew Temperaturedew Temperature
Air Air TemperatureTemperature
TT
Dew Dew TemperatureTemperature
TTdpdp
Actual Vapor in Actual Vapor in the airthe air
[gr per kg dry air][gr per kg dry air]
Relative Relative humidityhumidity
RHRH
8686ooFF 6464ooFF 10.8310.83 39%39%
7777ooFF 6060ooFF 10.8310.83 53%53%
6868ooFF ooFF 10.8310.83 72%72%
5959ooFF ooFF 10.8310.83 100%100%
![Page 21: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/21.jpg)
Quantum of energyQuantum of energy
![Page 22: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/22.jpg)
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 ff lm lm= (= (EEll – – EEmm ) /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))
![Page 23: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/23.jpg)
AvirisAvirisVisible and IR
![Page 24: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/24.jpg)
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
frequency
frequency
One molecule
Many molecules:pressure broaden*
*caused by collision between molecules
![Page 25: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/25.jpg)
Line shapesLine shapes
LorentzLorentz
GrossGross
Van-Vleck-WeisskoptVan-Vleck-Weisskopt
Liebe MPM model for Liebe MPM model for – Millimeter wave Millimeter wave
propagation model propagation model
22)(
1),(
lmlmL ff
ffF
22222 4)(
41),(
fff
ffffF
lm
lmlmG
2222
2
)()(
1),(
fffff
fffF
lmlmlmlmvw
![Page 26: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/26.jpg)
Absorption BandsAbsorption Bands Mainly water and oxygen for microwavesMainly water and oxygen for microwaves
Bri
ghtn
ess
Te
mp
era
ture
[K]
Bri
ghtn
ess
Te
mp
era
ture
[K]
Frequency [GHz]Frequency [GHz]
![Page 27: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/27.jpg)
Note how line width changes with height due to less pressure broadening
![Page 28: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/28.jpg)
![Page 29: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/29.jpg)
Total AtmosphericTotal Atmospheric AbsorptionAbsorptiongg, ,
Opacity Opacity , [Np] , [Np]
Loss factorLoss factor L L
[L en dB] [L en dB]
22 OOHg
o
e dzz
sec
sec)(0
0sec)(
secdzzg
o eeL
To convert from Np/km to dB/km multiply by 4.343 for 1-way propagation
![Page 30: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/30.jpg)
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
![Page 31: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/31.jpg)
Latent Heat Latent Heat – to understand radiation budget – to understand radiation budget
need to monitor water content in atmosphereneed to monitor water content in atmosphere
![Page 32: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/32.jpg)
Scattering from Scattering from Hydrometeors:Hydrometeors:
Clouds, Snow, RainClouds, Snow, Rain
![Page 33: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/33.jpg)
Outline: Clouds & RainOutline: Clouds & Rain
1.1. Single sphere (Single sphere (Mie vs. RayleighMie vs. Rayleigh))
2.2. Sphere of rain, snow, & ice (Sphere of rain, snow, & ice (HydrometeorsHydrometeors)) Find their Find their cc, n, ncc, , bb
3.3. Many spheres together : Clouds, Rain, SnowMany spheres together : Clouds, Rain, Snowa. Drop size distributiona. Drop size distribution
b. Volume Extinction= Scattering+ Absorptionb. Volume Extinction= Scattering+ Absorption
c. Volume Backscatteringc. Volume Backscattering
Radar Equation Radar Equation forfor Meteorology Meteorology
TTBB Brightness by Clouds & Rain Brightness by Clouds & Rain
![Page 34: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/34.jpg)
CloudsClouds Types on our Types on our AtmosphereAtmosphere
![Page 35: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/35.jpg)
Sizes for cloud and rain dropsSizes for cloud and rain drops
![Page 36: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/36.jpg)
%
Cirrus Clouds Composition
![Page 37: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/37.jpg)
EM interaction with EM interaction with Single Spherical Particles Single Spherical Particles
Absorption Absorption – Cross-Section, Cross-Section, QQa a =P=Pa a /S/Sii
– Efficiency, Efficiency, aa== QQa a //rr22
Scattered Scattered – Power, Power, PPs s
– Cross-section , Cross-section , QQs s =P=Ps s /S/Sii
– Efficiency,Efficiency, ss== QQs s //rr22
Total power removedTotal power removed by sphere from the incident EM by sphere from the incident EM wave, wave, e e = = ss+ + aa
BackscatterBackscatter, , SSss(() = S) = Siibb/4/4RR22
Si
![Page 38: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/38.jpg)
Mie Scattering: Mie Scattering: general solution to general solution to EM EM scattered, absorbed by dielectric scattered, absorbed by dielectric
sphere.sphere.
Uses 2 parameters Uses 2 parameters (Mie parameters)(Mie parameters)– Size wrt. Size wrt. : :
– Speed ratio on both media:Speed ratio on both media:
coλ
πrr 2
2
p
oc
cb
cp
b k
j
n
nn
)( p
![Page 39: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/39.jpg)
[Index of Refraction and [Index of Refraction and RefractivityRefractivity]]
The Propagation constant The Propagation constant depends on the relative depends on the relative complex permittivitycomplex permittivity
Where the index of Where the index of refraction is refraction is
But But n’n’airair≅≅1.0003 1.0003
So we define So we define NN
![Page 40: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/40.jpg)
So… So…
Propagation in terms of Propagation in terms of NN is is
And the attenuation and And the attenuation and phase is phase is
And the power density carried And the power density carried by wave traveling in the by wave traveling in the zz--direction is :direction is :
– With With ff in GHz in GHz
![Page 41: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/41.jpg)
Mie SolutionMie Solution
Mie solutionMie solution
Where Where aamm & b & bmm are the are the Mie coefficientsMie coefficients given by 8.33a to given by 8.33a to
8.33b in the textbook.8.33b in the textbook.
Probl 8.1-16, menos 7,9,10,13 para jueves Abr10Probl 8.1-16, menos 7,9,10,13 para jueves Abr10
}Re{)12(2
),(
)|||)(|12(2
),(
12
2
1
22
mm
ma
mm
ms
bamn
bamn
![Page 42: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/42.jpg)
Mie coefficientsMie coefficients
"'
1
1
1
1
cossin
}Re{}Re{
}Re{}Re{
jnnn
jWwhere
WWm
nA
WWm
nA
b
WWm
n
A
WWm
n
A
a
o
mmm
mmm
m
mmm
mmm
m
coλ
πrr 2
2
p
oc
cb
cp
b k
j
n
nn
)( p
![Page 43: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/43.jpg)
Mie RegionsMie RegionsRayleigh region
Intermediate or Mie region
Optical region
Example: sphere with =3.2(1-j)
Cambio de regiones de acuerdo a razon de ’”
Optical region
Intermediate region
Rayleigh region
Conclusion: regiones se definen de acuerdo a y a n
![Page 44: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/44.jpg)
Backscattering Backscattering
Rayleigh regionIntermediate or Mie
regionOptical region
![Page 45: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/45.jpg)
Variations of water dielectric const. with Variations of water dielectric const. with frequency and Temperaturefrequency and Temperature
![Page 46: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/46.jpg)
Non-absorbing Non-absorbing sphere or dropsphere or drop
((nn””==0 for 0 for a a perfect dielectricperfect dielectric, ,
which is awhich is anon-absorbingnon-absorbing sphere) sphere)
oook
k
jjnnn
call
o
)("'
Re
=.06
Rayleigh region |n|<<1
![Page 47: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/47.jpg)
Conducting (absorbing) sphereConducting (absorbing) sphere
=2.4
Rayleigh region
Intermediate or Mie region
Optical region
![Page 48: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/48.jpg)
Plots of Mie Plots of Mie ee versus versus
As As nn’’’’ increases, so does the absorption ( increases, so does the absorption (aa), and less is the ), and less is the
oscillatory behavior.oscillatory behavior. Optical limit (Optical limit (r r >>>>) is ) is ee =2. =2.
Crossover Crossover forfor – Hi conducting sphere at Hi conducting sphere at =2.4=2.4
– Weakly conducting sphere is at Weakly conducting sphere is at =.06=.06
Four Cases of sphere in air :
n=1.29 (lossless non-absorbing sphere)
n=1.29-j0.47 (low loss sphere)
n=1.28-j1.37 (lossy dielectric sphere)
n= perfectly conducting metal sphere
Rayleigh Intermediate Optical
![Page 49: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/49.jpg)
Rayleigh Approximation |Rayleigh Approximation |nn|<<1|<<1 Scattering efficiencyScattering efficiency
Extinction efficiencyExtinction efficiency
where K is the where K is the dielectric factordielectric factor
...||3
8}Im{4 24 KKe
...||3
8 24 Ks
2
1
2
12
2
c
c
n
nK
![Page 50: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/50.jpg)
Absorption efficiency in Absorption efficiency in Rayleigh regionRayleigh region
esea K }Im{4
i.e. scattering can be neglected in Rayleigh region(small particles with respect to wavelength)
|n|<<1
![Page 51: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/51.jpg)
Scattering from HydrometeorsScattering from Hydrometeors
Rayleigh Scattering Mie Scattering
>> particle size comparable to particle size--when rain or ice crystals are present. 33GHz (9mm)
95GHz (3mm)
![Page 52: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/52.jpg)
Rayleigh scattering (λ >d)
Mie scattering (λ ~ d)
Rayleigh Approximation Rayleigh Approximation for ice crystalsfor ice crystals
![Page 53: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/53.jpg)
![Page 54: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/54.jpg)
Single Particle Cross-sections Single Particle Cross-sections vs. vs.
Scattering cross sectionScattering cross section
Absorption cross sectionAbsorption cross section
In the Rayleigh region (In the Rayleigh region (nn<<1) =><<1) =>QQaa is larger, so is larger, so
much more of the signal is absorbed than much more of the signal is absorbed than scattered. Therefore scattered. Therefore
][m ||3
2 2262
KQs
][m }Im{ 232
KQa
For small drops, almost no scattering, i.e. no bouncing from drop since it’s so small.
![Page 55: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/55.jpg)
Gas molecules = much smaller than visible => Rayleigh approx. is OK.
Red 700nm
Violet 400nm
![Page 56: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/56.jpg)
Mie ScatteringMie Scattering
Mie scatt. is almost independent of frequencyMie scatt. is almost independent of frequency Cloud droplets ~20mm compare to 500nmCloud droplets ~20mm compare to 500nm Microwaves have Microwaves have ~cm or mm (large) – Rayleigh for most ~cm or mm (large) – Rayleigh for most
atmospheric constituentsatmospheric constituents Laser have Laser have ~nm - Mie~nm - Mie
dependent] [almost independent]
![Page 57: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/57.jpg)
![Page 58: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/58.jpg)
Observe scattering in Visible EMObserve scattering in Visible EM; ; forward scattering vs. backscatteringforward scattering vs. backscattering
Mie scattering by dust particles and aerosols
Rayleigh scattering by water vapor molecules and gases.
![Page 59: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/59.jpg)
![Page 60: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/60.jpg)
Mie forward scattering nos impide ver bien a menos que haya alto contraste.
![Page 61: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/61.jpg)
Forward scattering
![Page 62: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/62.jpg)
![Page 63: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/63.jpg)
Rayleigh-Mie-Geometric/OpticsRayleigh-Mie-Geometric/Optics Along with absorption, scattering is a major cause of the Along with absorption, scattering is a major cause of the
attenuation of radiation by the atmosphere for visible. attenuation of radiation by the atmosphere for visible. Scattering varies as a function of the ratio of the particle diameter to Scattering varies as a function of the ratio of the particle diameter to
the wavelength (the wavelength (d/d/) of the radiation.) of the radiation. When this ratio is less than about one-tenth (When this ratio is less than about one-tenth (d/d/), ), RayleighRayleigh
scattering occurs in which the scattering coefficient varies inversely scattering occurs in which the scattering coefficient varies inversely as the as the fourth powerfourth power of the wavelength. of the wavelength.
At larger values of the ratio of particle diameter to wavelength, the At larger values of the ratio of particle diameter to wavelength, the scattering varies in a complex fashion described by the scattering varies in a complex fashion described by the Mie theoryMie theory; ;
at a ratio of the order of 10 (at a ratio of the order of 10 (d/d/), the laws of ), the laws of geometric opticsgeometric optics begin to apply. begin to apply.
![Page 64: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/64.jpg)
Mie Scattering Mie Scattering (necessary if d/(necessary if d/), ), Mie theory : A complete mathematical-physical theory Mie theory : A complete mathematical-physical theory
of the scattering of electromagnetic radiation by of the scattering of electromagnetic radiation by spherical particles, developed by G. Mie in 1908. spherical particles, developed by G. Mie in 1908.
In contrast to Rayleigh scattering, the Mie theory In contrast to Rayleigh scattering, the Mie theory embraces all possible ratios of diameter to wavelength. embraces all possible ratios of diameter to wavelength. The Mie theory is very important in meteorological The Mie theory is very important in meteorological optics, where diameter-to-wavelength ratios of the optics, where diameter-to-wavelength ratios of the order of unity and larger are characteristic of many order of unity and larger are characteristic of many problems regarding haze and cloud scattering. problems regarding haze and cloud scattering.
When d/When d/ 1 1 neither Rayleigh or Geometric Optics neither Rayleigh or Geometric Optics Theory appliesTheory applies. Need to use Mie.. Need to use Mie.
Scattering of radar energy by raindrops constitutes Scattering of radar energy by raindrops constitutes another significant application of the Mie theory. another significant application of the Mie theory.
![Page 65: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/65.jpg)
Backscattering Cross-sectionBackscattering Cross-section From Mie solution, the backscattered field by a From Mie solution, the backscattered field by a
spherical particle isspherical particle is
Observe thatObserve that perfect dielectricperfect dielectric
(nonabsorbent) sphere (nonabsorbent) sphere
exhibits large exhibits large
oscillations for oscillations for >1.>1. Hi absorbing and perfect Hi absorbing and perfect
conducting spheres show conducting spheres show
regularly damped oscillations.regularly damped oscillations.
2
2
12
))(12(11
),(r
bamn bm
mm
mb
![Page 66: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/66.jpg)
Backscattering from metal Backscattering from metal spheresphere
5.0nfor
||4 24
Kb
Rayleigh Region defined asRayleigh Region defined as
For conducting sphere For conducting sphere
2
12
2
n
nK
Where,
![Page 67: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/67.jpg)
Scattering by HydrometeorsScattering by HydrometeorsHydrometeors (water particles)Hydrometeors (water particles) In the case of In the case of waterwater, the index of refraction is a , the index of refraction is a
function of function of T & fT & f. (fig 5.16). (fig 5.16)
@T=20C@T=20C
For ice.For ice. For snow, itFor snow, it’’s a mixture of both above. s a mixture of both above.
GHz 300 @ 47.4.2
GHz 30 @ 5.22.4
GHz 1 @ 25.9
'''
j
j
j
jnnnw
78.1' in
![Page 68: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/68.jpg)
Liquid water refractivity, nLiquid water refractivity, n’’
![Page 69: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/69.jpg)
Liquid water refractivity, nLiquid water refractivity, n””
![Page 70: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/70.jpg)
Sphere pol signatureSphere pol signature
Co-pol
Cross-pol
![Page 71: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/71.jpg)
Mie Efficiency at 3GHz and 30GHzMie Efficiency at 3GHz and 30GHz
![Page 72: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/72.jpg)
At 300GHzAt 300GHz
![Page 73: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/73.jpg)
![Page 74: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/74.jpg)
SnowflakesSnowflakes
Snow is mixture of ice crystals and airSnow is mixture of ice crystals and air
The relative permittivity of The relative permittivity of dry snowdry snow
The The KKdsds factor for dry snow factor for dry snow
0a3g/cm3.005.0 s
''
'
'
'
2
1
3
1
dsi
ds
i
s
ds
ds
5.01.1
i
i
ds
ds KK
2
1
i
iiK
24
652
4
652 ||
4
D ||
D i
ods
osbbs KKr
![Page 75: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/75.jpg)
Volume ScatteringVolume Scattering
Two assumptions:Two assumptions:– particles randomly distributed in volume-- particles randomly distributed in volume--
incoherentincoherent scattering theory. scattering theory.– Concentration is small-- ignore Concentration is small-- ignore shadowingshadowing..
Volume Scattering coefficient is the total Volume Scattering coefficient is the total scattering cross section per unit volumescattering cross section per unit volume..
rdrQrp ss )()( [Np/m]rdrrp bb )()( 222 / / / rrQrQ bbaass
DdDDN bb )()(
![Page 76: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/76.jpg)
Total number of drops per unit Total number of drops per unit volumevolume
DdDNrdrpNv )()(in units of mm-3
Disdrometer- measures DSD
http://www.powershow.com/view/143354-NzNhN/Thies_Laser_Precipitation_Monitor_for_precipitation_type_detection_powerpoint_ppt_presentation
Drop size distribution in terms of radius or diameter
![Page 77: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/77.jpg)
ppnn(r)(r) for Various Hydrometeors for Various Hydrometeors
![Page 78: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/78.jpg)
rdrQrp ss )()(
Volume ScatteringVolume Scattering
ItIt’’s also expressed ass also expressed as
or in dB/km units,or in dB/km units,
0
,,2
2
3
,, )()(8
dp beso
bes
[dB/km]
[Np/m]
DdDDN bbdB
0
3 )()(1034.4
ddrrQr o
sso 2 and / , /2 2 Using...
[s,e,b stand for scattering, extinction and backscattering.]
![Page 79: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/79.jpg)
24
652
322
24
652
||D
)Im(D
||3
D 2
wbb
waa
wss
Kr
KrQ
KrQ
For Rayleigh approximationFor Rayleigh approximation
Substitute eqs. 41, 44 and 46 into definitionsSubstitute eqs. 41, 44 and 46 into definitions of of the cross sectional areas of a scatterer.the cross sectional areas of a scatterer.
D=2r =diameter
![Page 80: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/80.jpg)
Noise in Stratus cloud imageNoise in Stratus cloud image--scanning Kscanning Kaa-band radar-band radar
![Page 81: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/81.jpg)
Volume Volume extinctionextinction from clouds from clouds Total attenuation is due to gases,cloud, and rainTotal attenuation is due to gases,cloud, and rain
cloud volume extinction is (eq.8.69)cloud volume extinction is (eq.8.69)
Liquid Water Content Liquid Water Content LWCLWC or or mmvv ) )
water density = 10water density = 1066 g/m g/m33
epcega
w
![Page 82: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/82.jpg)
Relation with Cloud water Relation with Cloud water contentcontent
This means extinction increases with cloud This means extinction increases with cloud water content.water content.
wherewhere
and wavelength is in cm.and wavelength is in cm.
![Page 83: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/83.jpg)
Volume Volume backscattering backscattering from from CloudsClouds
Many applications require the modeling of the Many applications require the modeling of the radar return.radar return.
For a For a singlesingle drop [Eq. 8.75 and 8.78] drop [Eq. 8.75 and 8.78]
For For manymany drops (cloud) drops (cloud)
![Page 84: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/84.jpg)
Reflectivity Factor, ZReflectivity Factor, Z
Is defined asIs defined as
so thatso that
and sometimes expressed in and sometimes expressed in dBZdBZ to cover a to cover a wider dynamic range of weather conditions. wider dynamic range of weather conditions.
Z is also used for rain and ice measurements.Z is also used for rain and ice measurements.
ZKwo
vc2
4
5
||
![Page 85: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/85.jpg)
Reflectivity in other booksReflectivity in other books
![Page 86: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/86.jpg)
Reflectivity & Reflectivity FactorReflectivity & Reflectivity FactorR
efle
ctiv
ity,
[cm
-1]
dB
Z fo
r 1
g/m
3
Reflectivity and reflectivity factor produced by 1g/m3 liquid water Divided into drops of same diameter. (from Lhermitte, 2002).
Z (in dB)
![Page 87: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/87.jpg)
Cloud detection vs. Cloud detection vs. frequencyfrequency
S Ka W
![Page 88: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/88.jpg)
Rain dropsRain drops
A) Raindrops are not tear-shaped, as most people think.B) Very small raindrops are almost spherical in shape.C) Larger raindrops become flattened at the bottom, like that of a hamburger bun, due to air resistance.D) Large raindrops have a large amount of air resistance, which makes them begin to become unstable.E) Very large raindrops split into smaller raindrops due to air resistance.
![Page 89: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/89.jpg)
Precipitation (Precipitation (RainRain))
Volume extinction [eq. 8.85-87]Volume extinction [eq. 8.85-87]
where where RRrr is rain rate in mm/hr is rain rate in mm/hr
[dB/km] and [dB/km] and bb are given by various model are given by various model can depend on polarization since large drops are can depend on polarization since large drops are
not spherical but ~oblong.not spherical but ~oblong.
0
22
3
)()(8
dp eo
er
Mie coefficients
brR1
1
[dB/km]
![Page 90: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/90.jpg)
ee= = specific extincspecific extinction coeff.tion coeff.
![Page 91: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/91.jpg)
W-band W-band UMass CPRS radarUMass CPRS radar
![Page 92: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/92.jpg)
Rain Rate [mm/hr]Rain Rate [mm/hr] If know the rain drop size distribution, each drop If know the rain drop size distribution, each drop
has a liquid water mass of has a liquid water mass of
total mass per unit area and timetotal mass per unit area and time
rainfall rate is depth of water per unit timerainfall rate is depth of water per unit time
a useful formulaa useful formula
dDDDNDvR tr3)()(6/
wDm 3
6
0
3 )()6/()()( dDvDNDdAdtdDDmDN tw
![Page 93: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/93.jpg)
ZKdDK ww2
4
562
4
5
||
D||
Volume Volume BackscatteringBackscattering for Rain for Rain
For many drops in a volume, if we use For many drops in a volume, if we use Rayleigh approximation Rayleigh approximation
Marshall and Palmer developedMarshall and Palmer developed
but need Mie for but need Mie for ff>10GHz.>10GHz.
dDbrvr
6.1200 rRZ
ewvr ZK 24
5
||
![Page 94: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/94.jpg)
Rain retrieval AlgorithmsRain retrieval Algorithms
Several types of algorithms used to retrieve rainfall rate Several types of algorithms used to retrieve rainfall rate with polarimetric radars; mainly with polarimetric radars; mainly
R(ZR(Zhh), ), R(ZR(Zhh, Z, Zdrdr)) R(KR(Kdpdp)) R(KR(Kdpdp, Z, Zdrdr))
where where
RR is rain rate, is rain rate,
ZZhh is the horizontal co-polar radar reflectivity factor, is the horizontal co-polar radar reflectivity factor,
ZZdrdr is the is the differential reflectivitydifferential reflectivity
KKdpdp is the is the differentialdifferential specific specific phasephase shift a.k.a. differential shift a.k.a. differential propagation phase, defined aspropagation phase, defined as
band Xfor 5.40)(ˆ
band Sfor 62.11)(ˆ
85.0
937.0
dpdp
dpdp
KKR
KKR
)(2
)()(
12
12
rr
rrK dpdp
dp
![Page 95: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/95.jpg)
Raindrops symmetryRaindrops symmetry
Differential Reflectivity
Zdr
![Page 96: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/96.jpg)
SnowSnow extinction coefficient extinction coefficient
Both scattering and absorption ( for Both scattering and absorption ( for f f < < 20GHz --Rayleigh)20GHz --Rayleigh)
for snowfall rates in the range of a few mm/hr, the for snowfall rates in the range of a few mm/hr, the scattering is negligible.scattering is negligible.
At higher frequencies,the Mie formulation should be At higher frequencies,the Mie formulation should be used.used.
The is smaller that rain for the same R, but is The is smaller that rain for the same R, but is higher for melting snow.higher for melting snow.
dDQdDQ sase 31034.4
se
![Page 97: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/97.jpg)
SnowSnow Volume Backscattering Volume Backscattering
Similar to rainSimilar to rain
sds
o
dsvs ZKdDK 24
562
4
5
||
D||
iss
s ZdDdDDNZ2
6i2
6s
1D
1)(D
![Page 98: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/98.jpg)
Radar equation for MeteorologyRadar equation for Meteorology For weather applicationsFor weather applications
for a volume for a volume
2
43
22
4 e
R
GPP oot
r dr
R
o
epceg
22
2pcR
V
vpoot
rR
ecGPP
2
2222
432
Vv
![Page 99: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/99.jpg)
Radar EquationRadar Equation
For power distribution For power distribution in the main lobe in the main lobe assumed to be assumed to be Gaussian functionGaussian function.. 2
22
22
2ln1024 RL
LcGPP vrpoooot
r
22
as here defined are losses catmospheriway - two theAndeL
lossesreceiver and
tyreflectiviradar
where,
r
v
L
![Page 100: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/100.jpg)
RadarRadar Equation Equation222
22
2ln1024 RLL
cGPP v
recatm
pooootr
RLLc
GPP
atmrec
prad
orad
oodBo
dBt
dBr
log20)2ln1024log(10log20log10log10log10
log10)log(10)log(10)log(2022
RRPP dBcp
dBt
dBr log20log10log10
RcdB=radar constant (including atmospheric
attenuation)
For calibrated target
![Page 101: Microwave Interactions with the Atmosphere](https://reader037.vdocument.in/reader037/viewer/2022110103/56814325550346895daf8d00/html5/thumbnails/101.jpg)
The ER-2 Doppler Radar (EDOP) aboard the high-altitude ER-2 aircraft is a dual-beam 9.6 GHz radar to measure reflectivity and wind structure in precipitation systems.
These data sets provided information on the structure of precipitation systems. This was from Hurricane Georges -1998 passing over the Dominican Rep. while being ripped apart by tall mountains. Extremely strong convection is noted over the mountains that produced huge amounts of rainfall.
EDOP flew in conjunction with radiometers. The combined radar/radiometer data sets was used to develop rain estimation algorithms for the Tropical Rainfall Measuring Mission (TRMM).