Microwave Interactions with
the Atmosphere
S. L. Cruz Pol
Electrical and Computer Engineering
University of Puerto Rico
1
Atmosphere composition
Typical Atmosphere in %
21
0.93
Ni
O2
Ar
Other components:
78
Carbon dioxide (CO2), Neon (Ne), Helium (He), Methane (CH4), Krypton (Kr),
Hydrogen (H2) and Water vapor (highly variable)
2
Atmospheric Constituents
3
Introduction
 Up to now, we have assumed lossless atm.
 For 1 GHz< f< 15 GHz ~lossless
 For higher frequencies, =>absorption bands
H2O
•22.235 GHz
•183.3 GHz
•IR & visible
O2
•50-70GHz
•118.7GHz
•IR & visible
4
Outline
I. The atmosphere: composition, profile
II. Gases: many molecules
1. Shapes(G, VVW, L): below 100GHz, up to 300GHz
e.g. H2O , O2
2. Total Atmospheric
Absorption kg, opacity tq, and atm-losses Lq
3. TB: Downwelling Emission by Atmosphere
Sky Temp= cosmic + galaxy
5
U.S. Standard Atmosphere
Thermosphere
(or Ionosphere) 1000-3000oF!
Mesopause
Mesosphere
no aircrafts here
o
too cold ~-90 F
Stratopause
10km
Stratosphere- no H2O or dust
ozone absorption of UV
warms air to ~40oF
Tropopause
Troposphere – clouds, weather
P= 1013 mbars
T= 300K
= 1013 HPa
6
Atmospheric Profiles
US Standard Atmosphere 1962
 Temperature
 To  az

T ( z )   T(11)
T  ( z  20)
 (11)
0  z  11 km
11 km  z  20 km
20km  z  32 km
 Density
rair ( z)  1.225e z / H
1
or
where H1  9.5km densityscale height
rair ( z)  1.225e z / 7.3[1  0.3sin(z / 7.3)]
 Pressure
P= nRT/V=rairRT/M or Poe-z/H3
where H3  7.7km Pressurescale height
7
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/H4
[g/m3]
where ro averages 7.72 in mid latitudes
and the total mass of water vapor in a
column of unit cross section is

M    r ( z ) dz  r o H 4
0
where H 4  between 2  2.5km water- vaporscale height
8
9
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
fml= (Em - El ) /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)
10
Line Shapes
Absorption
One molecule
frequency
Many molecules:
pressure broaden*
frequency
*caused by collision between molecules
k a ( f , f lm ) 
4f
Slm F ( f , f lm )
c
where,
– Slm is the line strength
– F(f,flm) is the line shape
LINE SHAPES
– Lorentz
– Gross
– Van-Vleck-Weisskopt
11
Line shapes
 Lorentz
 Gross
FL ( f , f lm ) 
FG ( f , f lm ) 
1

 ( f  f lm ) 2   2
4 ff lm
 ( f lm2  f 2 ) 2  4 f 2 2
1
 Van-Vleck-Weisskopt
2
1 f 



Fvw ( f , f lm )  

  f lm  ( f lm  f ) 2   2 ( f lm  f ) 2   2
12
Absorption Bands
Brightness Temperature [K]
 Mainly water and oxygen for microwaves
Frequency [GHz]
13
Total Atmospheric
 Absorption kg,
k g  k H O  kO
2
 Opacity tq,
2

t q   k e ( z ) secqdz
0
 secq t o
 Loss factor Lq

t o secq
Lq  e
 k g ( z ) secqdz
 e0
14
Atmospheric Emission
 For clear atmosphere

TDN  secq  k a ( z ' )T ( z ' )e t ( 0, z ') secq dz'
0
where

t (0, z ' )   k a ( z )dz
0
Also there is some background radiation
Textra  Tcos mic  Tgallactic
Tcos=2.7K from the Big Bang and Tgal~0 above 5GHz
15
Relative Humidity
Air
Temperature
Vapor air can
hold
Relative
humidity
27.6
Actual Vapor in
the air
[gr per kg dry air]
10.83
86oF
77oF
20.4
10.83
53%
68oF
14.9
10.83
72%
59oF
10.8
10.83
100%
39%
16
Aviris
17