Transcript Sea salt aerosols: Their generation and role in the

Microwave Emissivity of a
Vertically Inhomogeneous Sea-Foam Layer:
Application to the WindSat Retrieval Algorithm
Magdalena D. Anguelova, Karen St. Germain,
Craig Smith, Peter Gaiser, Richard Bevilacqua,
Nai-Yu Wang, Michael Bettenhausen
Remote Sensing Physics Branch
Naval Research Laboratory
21 September, 2004
WindSat forward model
 Radiative transfer equation:
TBV, H   [eTS  r (Tdown   TC )]  Tup
TB3,4   e[TS  (Tdown   TC )]
 Semi-empirical surface model:
e = er + Δe
 2-scale model for er;
 WindSat data for Δe.
r 1  e
Complete physical model
 Surface emissivity: e  (1  f )er  fe f
 Difficulties in modeling e:




Two-scale model limitations;
Limited knowledge for ef ;
Separate er and ef ;
High uncertainty for f ;
Sea foam
 Whitecaps
on the surface
 Bubble plumes
below the surface
Foam void fraction
fa 
Volume of air
Volume of mixture
Foam dielectric constant
 f  ( , f a )
ε'
ε"
6.8 GHz
18.7 GHz
37.0 GHz
Matching impedances
r  
air
 1 
seawater
Matching impedances
r  
air
 1 
seawater
air
foam (98%)
seawater
foam (10%)
Mechanisms of attenuation
Tdown
 Absorption:
 85%-90%;
 Small in bubble walls;
 Max at water boundary;
Tsc
 Scattering:
 10%-15%;
 λ-dependent.
Max bubble dia 2 cm
Min bubble dia 0.02 cm
F
GHz
λ0
cm
λf cm
fa= 98%
fa= 10%
6.8
4.4
3.2
0.60
10.7
2.8
2.1
0.41
18.7
1.6
1.31
0.28
23.8
1.3
1.1
0.26
37.0
0.8
0.72
0.20
λf cm
Foam-covered area
 Reflection/scattering terms;
 Emission terms.
TB
z=0
z = -d
TBf = TBfr ( , p) + TBsc ( , p) + TBUf ( , p) + TBDf ( , p) + TBfw ( , p)
Model requirements
 Vertically inhomogeneous layer;
 Absorption and scattering;
 Various contributions to foam emission.
Droppleman, 1970
Rosenkranz and Staelin, 1972
Raizer and colleagues
1982, 1992
Chen et al., 2003
Foam emission
Our choice
 Macro characteristics (layer);
 Vertically inhomogeneous (depth profile);
 Flat specular boundaries;
 Incoherent approach -- weak scattering;
 Ignore scattering term;
z=0
Air, ε0=1
Foam, ε (z)
z = -d
Water, ε
Void fraction profile
f a ( z )  a  e bz
z0
f a (0)  0.99
z  d
f a ( d )  0.01
Foam dielectric constant

 f ( z )   1 

3 f a ( z )(  1) 

1  2  f a ( z )(  1) 
Foam attenuation coefficient
 f ( z )  k0 Im  f ( z )
Foam refraction
2

sin


 f ( z )  arccos 1 

 f ( z)





Foam emission components
dTe   f ( z ). sec  f ( z ).Ts ( z )dz + diffuse scattering term
Ts ( z )  const
dz
Foam emission components
dTe   f ( z ). sec  f ( z ).Ts ( z )dz
0
TBUf ( , p)  mU Ts .   f ( z ). sec  f ( z ).e  U dz
d
0
TBDf ( , p)  mDTs .   f ( z ). sec  f ( z ).e  D dz
d
dz
Foam emission components
dTe   f ( z ). sec  f ( z ).Ts ( z )dz
0
TBUf ( , p)  mU Ts .   f ( z ). sec  f ( z ).e  U dz
d
0
TBDf ( , p)  mDTs .   f ( z ). sec  f ( z ).e  D dz
d
0
 U ( z ,0)    f ( z ' ). sec  f ( z ' )dz '
z'
z'
 D (d , z )    f ( z ' ). sec  f ( z ' )dz '
d
dz
Foam emission components
dTe   f ( z ). sec  f ( z ).Ts ( z )dz
0
TBUf ( , p)  mU Ts .   f ( z ). sec  f ( z ).e  U dz
dz
d
0
TBDf ( , p)  mDTs .   f ( z ). sec  f ( z ).e  D dz
d
mU 
1  1
1  12 L2f
z'
mD 
2
mU
Lf
d
L f  e l (  d , 0 )
0
 U ( z ,0)    f ( z ' ). sec  f ( z ' )dz '
z'
 D (d , z )    f ( z ' ). sec  f ( z ' )dz '
1, 2 ( , p)  r1, 2 ( , p)
2
Foam contributions
TBf 0
TBfw
TBDf
TBUf
TBfr
d/0  0.02
d =0/50
320 m
d/0= 0.25
d = 0/4
4 mm
TBf0= TBfr ( , p) + TBsc ( , p) + TBUf ( , p) + TBDf ( , p) + TBfw ( , p)
TBf over distribution of thickness
T
Bf 0
(t ) p(t )dt
d min
d min  0.015 cm  0 / 5037 GHz
d max  25 cm  50 6.8 GHz
  3.5 cm
  1.2
 ln t   2 
p (t ) 
exp 

2
2 2 
t 2

1

2

  ln
  2  2





  2  2
  ln 
2



16
Reising et al., 2002
12




Frequency
TBf 
d max
8
4
0
0
1
2
3
Foam Thickness (cm)
4
Foam emission
Foam emission
Necessary experiments
 Void fraction profile;
 Values for boundary conditions;
 Bubble size distribution;
 Thickness distribution;
 Azimuthal dependence.