Transcript Microwave Interactions with the Atmosphere Dr. Sandra Cruz Pol Microwave Remote Sensing INEL 6669 Dept.

Microwave Interactions with
the Atmosphere
Dr. Sandra Cruz Pol
Microwave Remote Sensing INEL 6669
Dept. of Electrical & Computer Engineering,
UPRM, Mayagüez, PR
Atmosphere composition
Typical Atmosphere in %
21
0.93
Ni
O2
Ar
78
Other components:
Carbon dioxide (CO2), Neon (Ne), Helium (He), Methane (CH4), Krypton (Kr),
Hydrogen (H2) and Water vapor (highly variable)
Air Constituents in Troposphere and
Stratosphere
 N2 78.1%, O2 20.9%, 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 ~10-8
absorbs UV-B, 9.6mm
 CFCl3, CF2CL2 … absorbs IR
Atm. CO2 Concentration
Last 200 years
Methane
H2O is less than 2% yet has
great effect in climate & weather
Radiative Transfer in Atmosphere
during Daytime
During daytime only. Nighttime is another story
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
•22.235 GHz
•183.3 GHz
•IR & visible
O2
•50-70GHz
•118.7GHz
•IR & visible
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
U.S. Standard Atmosphere
95/120km
Mesopause
Thermosphere
(or Ionosphere) 1000-3000oF!
Mesosphere
no aircrafts here
o
too cold ~-90 F
50/60km
8/15km
Stratopause
Stratosphere- no H2O or dust
ozone absorption of UV
warms air to ~40oF
Tropopause
Troposphere – clouds, weather
P= 1013 mbars
T= 300K
= 1013 HPa
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 in kg/m3
r air ( z )  1.225e  z / H
or
1
where H1  9.5km density scale height
r air ( z )  1.225e  z / 7.3[1  0.3 sin( z / 7.3)]
 Pressure
P= nRT/V=rairRT/M or Poe-z/H3
Rair= 2.87
where H 3  7.7km Pressure scale height
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 - vapor scale height
Relative Humidity
 Dew point temperature (dew=rocío)
– 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.
Equations for RH
Where e = pressure and exp means exponential ex
Relative Humidity (RH)
simplified equations
T is in Celsius
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
10.83
53%
68oF
14.9
10.83
72%
59oF
10.8
10.83
100%
Relative Humidity, RH
dew Temperature
Air
Temperature
T
Dew
Actual Vapor in
Temperature
the air
Tdp
[gr per kg dry air]
Relative
humidity
RH
86oF
64oF
10.83
39%
77oF
60oF
10.83
53%
68oF
oF
10.83
72%
59oF
oF
10.83
100%
Quantum of energy
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)
Visible and IR
Aviris
Line Shapes
k g = kO + k H O
x
k a ( f , flm ) =
Absorption
One molecule
frequency
Many molecules:
pressure broaden*
frequency
*caused by collision between molecules
2
4p f
SlmF( f , flm )
c
where,
– Slm is the line strength
– F(f,flm) is the line shape
LINE SHAPES
– Lorentz
– Gross
– Van-Vleck-Weisskopt
Line shapes
 Lorentz
 Gross
FL ( f , f lm ) 
FG ( f , f lm ) 
1

 ( f  f lm ) 2   2
4 fflm
 ( 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
 Liebe MPM model for
– Millimeter wave
propagation model
k O and k H O
x
2
Absorption Bands
Brightness Temperature [K]
 Mainly water and oxygen for microwaves
Frequency [GHz]
44
k O = 0.182 fN = 0.182 f å Si Fi
2
"
O2
i=1
44
k O = 0.182 fN = 0.182 f å Si Fi
2
"
O2
i=1
Note how line width
changes with height
due to less pressure
broadening
Total Atmospheric
 Absorption kg,
k g  k H O  kO
2
 Opacity tq, [Np]
2

t q   k e ( z ) sec qdz
0
 Loss factor Lq
 [L en dB]
To convert from Np/km to
dB/km multiply by 4.343 for
1-way propagation
 sec q t o

t o secq
Lq  e
e
 k g ( z ) secqdz
0
Atmospheric Emission
 For clear atmosphere

TDN  sec q  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
Latent Heat – to understand radiation budget
need to monitor water content in atmosphere
Scattering from
Hydrometeors:
Clouds, Snow, Rain
Outline: Clouds & Rain
1. Single sphere (Mie vs. Rayleigh)
2. Sphere of rain, snow, & ice (Hydrometeors)
Find their ec, nc, sb
3. Many spheres together : Clouds, Rain, Snow
a. Drop size distribution
b. Volume Extinction= Scattering+ Absorption
c. Volume Backscattering
4. Radar Equation for Meteorology
5. TB Brightness by Clouds & Rain
Clouds Types on our
Atmosphere
Sizes for cloud and rain drops
Cirrus Clouds
Composition
70
60
40
hexagonal
plates
bullet rosettes
30
dendrites
50
%
20
others
10
0
Ice Crystals
EM interaction with
Single Spherical Particles
 Absorption
Si
– Cross-Section, Qa =Pa /Si
– Efficiency, xa= Qa /r2
 Scattered
– Power, Ps
– Cross-section , Qs =Ps /Si
– Efficiency, xs= Qs /r2
 Total power removed by sphere from the
incident EM wave, xe = xs+ xa
 Backscatter, Ss() = Sisb/4R2
Mie Scattering: general solution to
EM scattered, absorbed by dielectric
sphere.
 Uses 2 parameters (Mie parameters)
– Size wrt. l :
2r
2πr


ec
lp
λo
– Speed ratio on both media:
n
np
nb

e pc
e bc
(   j )
 ec 
ko
[Index of Refraction and
Refractivity]
 The Propagation constant
depends on the relative
complex permittivity
g = jw moeo e = j
 Where the index of
refraction is n2 = e
e = n = n'- jn"
w
c
e
 But n’air≅1.0003
 So we define N
n =1+10-6 N
N = N '- jN"
n' = 1+10 -6 N '
n" = 10 -6 N"
So…
Propagation in terms of N is
g=j
w
c
 And the power density
carried by wave traveling
in the z-direction is :
( n'- jn")
S(z) = Soe-2az = Soe-k az
And the attenuation and
phase is
a = Re[g ] =
b = Im[g ] =
w
c
w
c
n" = 10
n' =
w
-6
w
c
k a dB = 2a dB
N"
1+10
(
c
-6
N ')
-6
= 2 ´ 4.34 ´10 ´10 ´
3
= 0.182 fN"
– With f in GHz
w
c
N"
Mie Solution
 Mie solution
x s (n,  ) 
x a ( n,  ) 
2
2
2

2

2
2
(
2
m

1
)(|
a
|

|
b
|
)

m
m
m 1

 (2m  1) Re{a
m 1
m
bm }
 Where am & bm are the Mie coefficients given by
8.33a to 8.33b in the textbook.
 Probl 8.1-16, menos 7,9,10,13 para jueves Abr10
Mie coefficients
 Am m 
  Re{Wm }  Re{Wm 1}

n 

am 
 Am m 
 Wm  Wm 1

 n 
2r
2πr


ec
lp
λo

m
 nAm   Re{Wm }  Re{Wm 1}


e pc
np
(   j )
bm 
n



e


c
m
n
ko
e
nA

W

W
 m
 m
b
bc
m 1


where
Wo  sin   j cos 
n  n '  jn"
Mie Regions
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  y a n
Backscattering
Rayleigh region
Intermediate or Mie
region
Optical region
Variations of water dielectric const. with
frequency and Temperature
Non-absorbing
sphere or drop
(n”=0 for
a perfect dielectric,
which is a
non-absorbing sphere)
Re call
(   j )
n  n' jn" 
ko
k o   m oe o
Rayleigh region |n|<<1
 =.06
Conducting (absorbing) sphere
Rayleigh Intermediate or Mie
region
region
 =2.4
Optical region
Rayleigh
Plots of Mie xe versus 
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  =2.4
– Weakly conducting sphere is at  =.06
Rayleigh Approximation |n|<<1
 Scattering efficiency
8 4
x s   | K |2 ...
3
 Extinction efficiency
8 4
x e  4  Im{  K }   | K |2 ...
3
 where K is the dielectric factor
n2 1 e c 1
K 2

n  2 ec  2
Absorption efficiency in
Rayleigh region
x a  xe  x s  4 Im{  K}  xe
i.e. scattering can be neglected in Rayleigh region
(small particles with respect to wavelength)
|n|<<1
Scattering from Hydrometeors
Rayleigh Scattering
l >> particle size
95GHz (3mm)
33GHz (9mm)
Mie Scattering
l comparable to particle size
--when rain or ice crystals are
present.
Rayleigh Approximation
for ice crystals
Rayleigh scattering
(λ >d)
Mie scattering
(λ ~ d)
Single Particle Cross-sections
vs. 
 Scattering cross section
2l2 6
Qs 
 | K |2 [m 2 ]
3
For small drops, almost
no scattering, i.e. no
bouncing from drop
since it’s so small.
 Absorption cross section
l2 3
Qa   Im{ K } [m 2 ]

In the Rayleigh region (n<<1) =>Qa is larger,
so much more of the signal is absorbed than
scattered. Therefore
x s << x a
Gas molecules = much smaller than visible l=> Rayleigh approx. is OK.
Red
700nm
Violet
400nm
Mie Scattering
[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
Observe scattering in Visible EM;
forward scattering vs. backscattering
Mie
scattering
by dust
particles
and
aerosols
Rayleigh
scattering
by water
vapor
molecules
and gases.
Mie forward
scattering
nos impide
ver bien a
menos que
haya alto
contraste.
Forward scattering
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.
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  1 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.
Backscattering Cross-section
 From Mie solution, the backscattered
field by a spherical particle is
2
sb
x b (n,  )  2   1 (2m  1)(am bm )  2
 m1
r
1

m
Observe that

perfect dielectric
(nonabsorbent) sphere
exhibits large
oscillations for >1.

Hi absorbing and perfect
conducting spheres show
regularly damped oscillations.
Backscattering from metal
sphere
 Rayleigh Region defined as
x b  4  4 | K |2
for n < 0.5
Where,
4
x
=
9
c
For conducting sphere b
n2 1
K 2
n 2
for n = ¥and c <<1
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
 9  j.25 @ 1 GHz

nw  n' jn' '   4.2  j 2.5 @ 30 GHz
2.4  j.47 @ 300 GHz

 For ice. n'i  1.78
 For snow, it’s a mixture of both above.
Liquid water refractivity, n’
Liquid water refractivity, n”
Sphere pol signature
Co-pol
Cross-pol
Mie Efficiency at 3GHz and 30GHz
At 300GHz
Snowflakes
 Snow is mixture of ice crystals and air
3
3
ri = 0.916 g/cm r a  0 0.05  r s  0.3g/cm
 The relative permittivity of dry snow
e ds'  1 r s  e ds'  1 

  '
'
' 
3e ds
ri  e i  2e ds 
 The Kds factor for dry snow
K ds
r ds

1.1K i
ri
 0.5
s bs  x brs 2
ei 1
Ki 
ei  2
5
6
 5 D6

D
2
2

|
K
|

|
K
|
ds
i
l4 o
4l4 o
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.
kkbskb pp((rN
sr))bdd(rrD)d D
r))s(QD
bs()(r
x s  Qs / r 2
x a  Qa / r 2
[Np/m]
x b  s b / r 2
Total number of drops per unit
volume
N v   p (r )d r   N ( D)d D
in units of mm-3
Drop size distribution in terms of radius or diameter
a -br g
p(r ) = ar e
-D/Do
N(D) = Noe
http://www.powershow.com/view/143354NzNhN/Thies_Laser_Precipitation_Monitor_for_prec
ipitation_type_detection_powerpoint_ppt_presentati
on
Disdrometer- measures DSD
pn(r) for Various Hydrometeors
Volume Scattering
Using...
lo
  2r / lo , x s  Qs / r and dr 
d
2
2
 It’s also expressed as
3 
o
2
0
l
2
k

p
(
r
)
Q
(
r
)
d
r
k s ,se,b 

p
(

)
x s , e ,b (  ) d 
s

8
[Np/m]
[s,e,b stand for scattering, extinction and backscattering.]
 or in dB/km units,

 dB   b  4.34 103  N ( D)s b ( D)d D
0
[dB/km]
For Rayleigh approximation
 Substitute eqs. 41, 44 and 46 into definitions of
the cross sectional areas of a scatterer.
5
6
2

D
2
Qs  x sr 2 
|
K
|
w
4
3l
2
3
 D
2
Qa  x ar 
Im(  K w )
l
5
6

D
2
2
s b  x br 
| Kw |
4
l
D=2r =diameter
Noise in Stratus cloud image
-scanning Ka-band radar
Volume extinction from clouds
 Total attenuation is due to gases,cloud, and rain
k a  k g  k e c  k ep
 cloud volume extinction is (eq.8.69)
p
8p
3
3
k ec = ò QadD = Im{-Kw } ò D dD =
Im{-K}å ri
lo
lo
i=1
2
2
 Liquid Water Content LWC or mv )
4p 3
6 p
mv = rw å ri =10
6
i=1 3
Nv

rw 
water density = 106 g/m3
3
D
ò dD
Nv
Relation with Cloud water
content
 This means extinction increases with cloud
water content.
k ec = k L mv
where
k L = .434
6p
lo
Im(-K)
and wavelength is in cm.
-1 -1
3
[dBkm g m ]
Volume backscattering from
Clouds
 Many applications require the modeling of the
radar return.
 For a single drop [Eq. 8.75 and 8.78]
5
6
5 6
p
D
2
64
p
r
2
s b = x bp r 2 =
K
=
K
l4
l4
 For many drops (cloud)
p5
2
h = s vc = ò s b N(D)dD = 4 K
l
N
5
5
p
p
2
2
6
h = 4 K å Di = 4 K Z
l
l
i=1
V
ò N(D)D
6
dD =
Reflectivity Factor, Z
Z=
 Is defined as
ò
NV
D6 N(D)dD = å Di6
i=1
so that
s vc
5
 4 | K w |2 Z
lo
 and sometimes expressed in dBZ to cover a
wider dynamic range of weather conditions.
dBZ =10 log Z
 Z is also used for rain and ice
measurements.
Reflectivity in other books
5
p
h = 10 -12 4 | K w |2 Z
lo
where h is in cm -1, l in cm and
Z is expressed in mm 6 /m 3
Reflectivity & Reflectivity Factor
Z (in dB)
dBZ for 1g/m3
Reflectivity,  [cm-1]

Reflectivity and reflectivity factor produced by 1g/m3 liquid water
Divided into drops of same diameter. (from Lhermitte, 2002).
Cloud detection vs. frequency
S
Ka
W
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.
Precipitation (Rain)
 Volume extinction [eq. 8.85-87]
3 
o
2
0
l
k er 
8
b

p
(

)
x
(

)
d

 k 1 Rr
e

2
[dB/km]
Mie coefficients
 where Rr is rain rate in mm/hr
 k1 [dB/km] and b are given by various model
 can depend on polarization since large
drops are not spherical but ~oblong.
ke= specific extinction coeff.
k e = k1R
b
r
ì
-5 2.03
6.39
´10
f
for f < 2.9GHz
ï
ï 4.21´10 -5 f 2.42 for 2.9 £ f £ 54GHz
kl = í
-2 0.699
4.09
´10
f
for 54 £ f £ 180GHz
ï
ï
-0.151
3.38
f
for 180 GHz £ f
î
ì
.158
0.851
f
for f < 8.5GHz
ï
ï 1.41 f -0.0779 for 8.5 £ f £ 25GHz
b=í
-0.272
for 25 £ f £ 164GHz
ï 2.63 f
ï
0.0126
0.616
f
for 164 GHz £ f
î
W-band UMass CPRS radar
Marshall - Palmer(1948)
-bD
N(D) = N0 e
-
N(D) = 8´10 e
6
R =rain in mm/hr
D= drop diameter in m
N=# drops per volume
4100
D
0.21
R
Rain Rate [mm/hr]
 If know the rain drop size distribution, each drop

has a liquid water mass of
m  D3 r w
6
 total mass per unit area and time

3
N
(
D
)
m
(
D
)
dD
dAdt

(
r

/
6
)
D
w

 N ( D)vt dD
0
 rainfall rate is depth of water per unit time
Rr   / 6 vt ( D) N ( D) D dD
3
 a useful formula
(-6.8D2 +4.88D) ù
é
vt (D) = 9.25ë1-e
û
Volume Backscattering for Rain
 For many drops in a volume, if we use
Rayleigh approximation
s vr
5
5

  s br dD  4 | K w |2  D 6 dD  4 | K w |2 Z
l
l
 Marshall and Palmer developed
Z  200 Rr1.6
 but need Mie for f>10GHz.
s vr

 4 | K w |2 Z e
l
5
Rain retrieval Algorithms
Several types of algorithms used to retrieve rainfall rate
with polarimetric radars; mainly
 R(Zh),
0.937
ˆ
R( K dp )  11.62 K dp for S band
 R(Zh, Zdr)
0.85
 R(Kdp)
Rˆ ( K dp )  40.5K dp
for X band
 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
 dp (r2 )   dp (r1 )
K dp 
2(r2  r1 )
Raindrops symmetry
Differential Reflectivity
Zdr
Snow extinction coefficient
 Both scattering and absorption
for f < 20GHz --Rayleigh)
k e s  4.34 10
3
(
[ Q dD   Q dD
a
s
 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 k e s is smaller that rain for the same R, but
is higher for melting snow.
Snow Volume Backscattering
 Similar to rain
s vs
5
5
2
6
 4 | K ds |  D dD  4 | K ds |2 Z s
l
lo
Z s   D s N ( D )dD 
6
1
r
2
s
D
6
i
dD 
1
r
2
s
Zi
Radar equation for Meteorology
 For weather applications
t   k g  k e c  k ep dr
R
Pt G l
 2t
Pr 
se
4  R
2 2
o o
3 4
o
 for a volume s  s vV
Pr 
Pt G l  ct p e
2 2
o o
2
324R 
2
2t
sv
 R 
V 

 2 
2
 ct p 


 2 
Radar Equation
 For power distribution
in the main lobe
assumed to be
Gaussian function.
Pr 
Pt Go2 l2oq oo ct p Lr
1024 ln 2
2
2
L
sv
R2
where,
s v    radar reflectivi ty
and Lr  receiver losses
And the two - way atmospheri c losses are defined here as
L2  e  2t
Radar Equation
Pr
dB
 Pt
dB
Pr 
 2GodB  20 log( lo )  10 log( q o
rad
Pt Go2l2oq oo ct p
sv
1024 ln 2 Latm Lrec
R2
2
2
)  10 log( o
rad
)  10 log t p
 10 log   10 log c  10 log Lrec  20 log Latm  10 log( 1024 2 ln 2)  20 log R
Pr
dB
 Pt
dB
 10 log t p  10 log   RcdB  20 log R
For calibrated target
RcdB=radar constant (including atmospheric
attenuation)
The ER-2 Doppler Radar
(EDOP)
aboard the high-altitude
ER-2 aircraft is a dualbeam 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).