1. Microwave Interactions with the Atmosphere
INEL 6069,
Microwave Interactions with the Atmosphere
Dr. Sandra Cruz Pol
Microwave Remote Sensing INEL 6669
Dept. of Electrical & Computer Engineering,
UPRM, Mayagüez, PR

2. Atmosphere composition
INEL 6069,
Atmosphere composition
Other components:
Carbon dioxide (CO2), Neon (Ne), Helium (He), Methane (CH4), Krypton (Kr), Hydrogen (H2) and Water vapor (highly variable)

3. Air Constituents in Troposphere and Stratosphere
N %, O %, H2O 0-2%
Inert gases 0.938%
Many of the least abundant have a disproportionally large influence on atmospheric transmission.
CO2 398ppm absorbs 2.8, 4.3 & 15 mm
CH4 1.7ppm absorbs 3.3 & 7.8mm
N2O .35ppm absorbs 4.5, 7.8 & 17mm
O3 ~ absorbs UV-B, 9.6mm
CFCl3, CF2CL2 … absorbs IR

4. Atm. CO2 Concentration
Last 200 years

6. Methane

9. H2O is less than 2% yet has great effect in climate & weather

10. Radiative Transfer in Atmosphere during Daytime
INEL 6069,
During daytime only. Nighttime is another story

11. Atm. Gases & Electromagnetic propagation
INEL 6069,
Atm. Gases & Electromagnetic propagation
Up to now, we have assumed lossless atm.
For 1 GHz< f< 15 GHz ~lossless
For higher frequencies, =>absorption bands
H2O O2
GHz
183.3 GHz
IR & visible
50-70GHz
118.7GHz
IR & visible

12. Outline I. The atmosphere: composition, profile
INEL 6069,
Outline
I. The atmosphere: composition, profile
II. Gases: many molecules
1. Shapes(G, VVW, L): below 100GHz, up to 300GHz
we find interaction with H2O and O2
2. Total Atmospheric
Absorption kg, opacity tq, and atm-losses Lq
3. TB: Downwelling Emission by Atmosphere
Sky Temp= cosmic + galaxy

13. U.S. Standard Atmosphere
INEL 6069,
U.S. Standard Atmosphere
Thermosphere
(or Ionosphere) oF!
95/120km
Mesopause
Mesosphere
no aircrafts here
too cold ~-90oF
50/60km
Stratopause
Stratosphere- no H2O or dust
ozone absorption of UV
warms air to ~40oF
8/15km
Tropopause
Troposphere – clouds, weather
P= 1013 mbars
= 1013 HPa
T= 300K

14. Atmospheric Profiles US Standard Atmosphere 1962
INEL 6069,
Atmospheric Profiles US Standard Atmosphere 1962
Temperature
Density in kg/m3
Pressure P= nRT/V=rairRT/M or Poe-z/H3 or
Rair= 2.87

15. INEL 6069,
Water 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)
rv(z)= roe-z/H [g/m3]
where ro averages in mid latitudes
and the total mass of water vapor in a
column of unit cross section is

16. Relative Humidity Dew point temperature (dew=rocío) Relative Humidity
is the T below which the WV in a volume of humid air at a constant barometric P will condense into liquid water.
Is the T as which fog forms
Relative Humidity
When Tair is close to Tdew => high %RH
Absolute Humidity, the mass of water per unit volume of air.

17. Equations for RH
Where e = pressure and exp means exponential ex

18. Relative Humidity (RH) simplified equations
T is in Celsius

19. Relative Humidity, RH vapor in air
INEL 6069,
Relative Humidity, RH vapor in air
Air Temperature T
Vapor air can hold
Actual Vapor in the air
[gr per kg dry air]
Relative humidity RH
86oF
27.6
10.83
39%
77oF
20.4
53%
68oF
14.9
72%
59oF
10.8
100%

20. Relative Humidity, RH dew Temperature
INEL 6069,
Relative Humidity, RH dew Temperature
Air Temperature T
Dew Temperature
Tdp
Actual Vapor in the air
[gr per kg dry air]
Relative humidity RH
86oF
64oF
10.83
39%
77oF
60oF
53%
68oF oF
72%
59oF
100%

21. Quantum of energy
INEL 6069,

22. EM interaction with Molecules
INEL 6069,
EM interaction with Molecules
Total internal energy state for a molecule
electronic energy corresponding to atomic level
vibration of atoms about their equilibrium position
rotation of atoms about center of molecule
E = Ee + Ev + Er
Bohr condition f lm= (El – Em ) /h
Values for energy differences for
electronic: 2 to 10 eV
vibrational-rotational: 0.1 to 2 eV
pure rotational: 10-4 to 5 x 10-2 eV ( microwaves)

23. INEL 6069,
Aviris
Visible and IR

24. Line Shapes where, Slm is the line strength F(f,flm) is the line shape
INEL 6069,
Line Shapes
where,
Slm is the line strength
F(f,flm) is the line shape
LINE SHAPES
Lorentz
Gross
Van-Vleck-Weisskopt
One molecule
frequency
Absorption
Many molecules:
pressure broaden*
frequency
*caused by collision between molecules

25. Line shapes Lorentz Gross Van-Vleck-Weisskopt Liebe MPM model for
INEL 6069,
Line shapes
Lorentz
Gross
Van-Vleck-Weisskopt
Liebe MPM model for
Millimeter wave propagation model

26. Absorption Bands Mainly water and oxygen for microwaves
INEL 6069,
Absorption Bands
Mainly water and oxygen for microwaves
Brightness Temperature [K]
Frequency [GHz]

27. Note how line width changes with height due to less pressure broadening

29. Total Atmospheric Absorption kg, Opacity tq, [Np] Loss factor Lq
INEL 6069,
Total Atmospheric
Absorption kg,
Opacity tq, [Np]
Loss factor Lq
[L en dB]
To convert from Np/km to dB/km multiply by for 1-way propagation

30. Atmospheric Emission For clear atmosphere where
INEL 6069,
Atmospheric Emission
For clear atmosphere
where
Also there is some background radiation
Tcos=2.7K from the Big Bang and Tgal~0 above 5GHz

31. Latent Heat – to understand radiation budget need to monitor water content in atmosphere
Radiative Transfer,
INEL 6069,

32. Scattering from Hydrometeors: Clouds, Snow, Rain

33. Outline: Clouds & Rain Single sphere (Mie vs. Rayleigh)
Sphere of rain, snow, & ice (Hydrometeors)
Find their ec, nc, sb
Many spheres together : Clouds, Rain, Snow
a. Drop size distribution
b. Volume Extinction= Scattering+ Absorption
c. Volume Backscattering
Radar Equation for Meteorology
TB Brightness by Clouds & Rain

34. Clouds Types on our Atmosphere

35. Sizes for cloud and rain drops

36. Cirrus Clouds Composition%
Cirrus Clouds Composition

37. EM interaction with Single Spherical Particles
Absorption
Cross-Section, Qa =Pa /Si
Efficiency, xa= Qa /pr2
Scattered
Power, Ps
Cross-section , Qs =Ps /Si
Efficiency, xs= Qs /pr2
Total power removed by sphere from the incident EM wave, xe = xs+ xa
Backscatter, Ss(p) = Sisb/4pR2

38. Mie Scattering: general solution to EM scattered, absorbed by dielectric sphere.
Uses 2 parameters (Mie parameters)
Size wrt. l :
Speed ratio on both media:

39. [Index of Refraction and Refractivity]
The Propagation constant depends on the relative complex permittivity
Where the index of refraction is
But n’air≅1.0003
So we define N

40. So… Propagation in terms of N is And the attenuation and phase is
And the power density carried by wave traveling in the z-direction is :
With f in GHz

41. Mie Solution Mie solution
Where am & bm are the Mie coefficients given by 8.33a to 8.33b in the textbook.
Probl , menos 7,9,10,13 para jueves Abr10

42. Mie coefficients

43. Mie Regions Cambio de regiones de acuerdo a razon de e’/e”
Rayleigh region
Intermediate or Mie region
Optical region
Rayleigh region
Intermediate region
Optical region
Cambio de regiones de acuerdo a razon de e’/e”
Example: sphere with
e =3.2(1-j)
Conclusion: regiones se definen de acuerdo a c y a n

44. Intermediate or Mie region
Backscattering
Intermediate or Mie region
Optical region
Rayleigh region

45. Variations of water dielectric const. with frequency and Temperature

46. Non-absorbing sphere or drop (n”=0 for a perfect dielectric, which is a non-absorbing sphere)
Rayleigh region |nc|<<1

47. Conducting (absorbing) sphere
Optical region
Rayleigh region
Intermediate or Mie region
c =2.4

48. Plots of Mie xe versus c
Rayleigh
Intermediate
Optical
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
As n’’ increases, so does the absorption (xa), and less is the oscillatory behavior.
Optical limit (r >>l) is xe =2.
Crossover for
Hi conducting sphere at c =2.4
Weakly conducting sphere is at c =.06

49. Rayleigh Approximation |nc|<<1
Scattering efficiency
Extinction efficiency
where K is the dielectric factor

50. Absorption efficiency in Rayleigh region
i.e. scattering can be neglected in Rayleigh region
(small particles with respect to wavelength)
|nc|<<1

51. Scattering from Hydrometeors
Rayleigh Scattering
Mie Scattering
 >> particle size
comparable to particle size
--when rain or ice crystals are present.
95GHz (3mm)
33GHz (9mm)

52. Rayleigh Approximation for ice crystals
Rayleigh scattering
(λ >d)
Mie scattering
(λ ~ d)

54. Single Particle Cross-sections vs. c
Scattering cross section
Absorption cross section
In the Rayleigh region (nc<<1) =>Qa is larger, so much more of the signal is absorbed than scattered. Therefore
For small drops, almost no scattering, i.e. no bouncing from drop since it’s so small.

55. Gas molecules = much smaller than visible l=> Rayleigh approx. is OK.
Red 700nm
Violet 400nm

56. Mie Scattering Mie scatt. is almost independent of frequency
[l dependent] [almost l independent]
Mie scatt. is almost independent of frequency
Cloud droplets ~20mm compare to 500nm
Microwaves have l~cm or mm (large) – Rayleigh for most atmospheric constituents
Laser have l~nm - Mie

58. Observe scattering in Visible EM; forward scattering vs. backscattering
Mie scattering by dust particles and aerosols
Rayleigh scattering by water vapor molecules and gases.

60. Mie forward scattering nos impide ver bien a menos que haya alto contraste.

61. Forward scattering

63. Rayleigh-Mie-Geometric/Optics
Along with absorption, scattering is a major cause of the attenuation of radiation by the atmosphere for visible.
Scattering varies as a function of the ratio of the particle diameter to the wavelength (d/l) of the radiation.
When this ratio is less than about one-tenth (d/l<1/10), Rayleigh scattering occurs in which the scattering coefficient varies inversely as the fourth power of the wavelength.
At larger values of the ratio of particle diameter to wavelength, the scattering varies in a complex fashion described by the Mie theory;
at a ratio of the order of 10 (d/l>10), the laws of geometric optics begin to apply.

64. Mie Scattering (necessary if d/l1),
Mie theory : A complete mathematical-physical theory of the scattering of electromagnetic radiation by spherical particles, developed by G. Mie in 1908.
In contrast to Rayleigh scattering, the Mie theory embraces all possible ratios of diameter to wavelength. The Mie theory is very important in meteorological optics, where diameter-to-wavelength ratios of the order of unity and larger are characteristic of many problems regarding haze and cloud scattering.
When d/l neither Rayleigh or Geometric Optics Theory applies. Need to use Mie.
Scattering of radar energy by raindrops constitutes another significant application of the Mie theory.

65. Backscattering Cross-section
From Mie solution, the backscattered field by a spherical particle is
Observe that
perfect dielectric
(nonabsorbent) sphere
exhibits large
oscillations for c>1.
Hi absorbing and perfect
conducting spheres show
regularly damped oscillations.

66. Backscattering from metal sphere
Rayleigh Region defined as
For conducting sphere
Where,

67. Scattering by Hydrometeors
Hydrometeors (water particles)
In the case of water, the index of refraction is a function of T & f. (fig 5.16)
@T=20C
For ice.
For snow, it’s a mixture of both above.

68. Liquid water refractivity, n’

69. Liquid water refractivity, n”

70. Sphere pol signature
Co-pol
Cross-pol

71. Mie Efficiency at 3GHz and 30GHz

72. At 300GHz

74. Snowflakes Snow is mixture of ice crystals and air
The relative permittivity of dry snow
The Kds factor for dry snow

75. Volume Scattering Two assumptions:
particles randomly distributed in volume-- incoherent scattering theory.
Concentration is small-- ignore shadowing.
Volume Scattering coefficient is the total scattering cross section per unit volume.
[Np/m]

76. Total number of drops per unit volume
in units of mm-3
Drop size distribution in terms of radius or diameter
Disdrometer- measures DSD

77. pn(r) for Various Hydrometeors

78. Volume Scattering It’s also expressed as or in dB/km units, Using...
[Np/m]
[s,e,b stand for scattering, extinction and backscattering.]
[dB/km]

79. For Rayleigh approximation
Substitute eqs. 41, 44 and 46 into definitions of the cross sectional areas of a scatterer.
D=2r =diameter

80. Noise in Stratus cloud image -scanning Ka-band radar

81. Volume extinction from clouds
Total attenuation is due to gases,cloud, and rain
cloud volume extinction is (eq.8.69)
Liquid Water Content LWC or mv )
water density = 106 g/m3

82. Relation with Cloud water content
This means extinction increases with cloud water content.
where
and wavelength is in cm.

83. Volume backscattering from Clouds
Many applications require the modeling of the radar return.
For a single drop [Eq and 8.78]
For many drops (cloud)

84. Reflectivity Factor, Z Is defined as so that
and sometimes expressed in dBZ to cover a wider dynamic range of weather conditions.
Z is also used for rain and ice measurements.

85. Reflectivity in other books

86. Reflectivity & Reflectivity Factorh
Z (in dB)
Reflectivity, h [cm-1]
dBZ for 1g/m3
Reflectivity and reflectivity factor produced by 1g/m3 liquid water
Divided into drops of same diameter. (from Lhermitte, 2002).

87. Cloud detection vs. frequency
S Ka W

88. Rain 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.

89. Precipitation (Rain) Volume extinction [eq. 8.85-87]
where Rr is rain rate in mm/hr
[dB/km] and b are given by various model
can depend on polarization since large drops are not spherical but ~oblong.
[dB/km]
Mie coefficients

90. ke= specific extinction coeff.

91. W-band UMass CPRS radar

92. Rain Rate [mm/hr]
If know the rain drop size distribution, each drop has a liquid water mass of
total mass per unit area and time
rainfall rate is depth of water per unit time
a useful formula

93. Volume Backscattering for Rain
For many drops in a volume, if we use Rayleigh approximation
Marshall and Palmer developed
but need Mie for f>10GHz.

94. Rain retrieval Algorithms
Several types of algorithms used to retrieve rainfall rate with polarimetric radars; mainly
R(Zh),
R(Zh, Zdr)
R(Kdp)
R(Kdp, Zdr)
where
R is rain rate,
Zh is the horizontal co-polar radar reflectivity factor,
Zdr is the differential reflectivity
Kdp is the differential specific phase shift a.k.a. differential propagation phase, defined as

95. Raindrops symmetry
Differential Reflectivity
Zdr

96. Snow extinction coefficient
Both scattering and absorption ( for f < 20GHz --Rayleigh)
for snowfall rates in the range of a few mm/hr, the scattering is negligible.
At higher frequencies,the Mie formulation should be used.
The is smaller that rain for the same R, but is higher for melting snow.

97. Snow Volume Backscattering
Similar to rain

98. Radar equation for Meteorology
For weather applications
for a volume

99. Radar Equation
For power distribution in the main lobe assumed to be Gaussian function.

100. Radar Equation For calibrated target
RcdB=radar constant (including atmospheric attenuation)

101. These data sets provided information on the structure of precipitation systems.
This was from Hurricane Georges 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).
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.