Modeling polarized radiation for CLARREO inter- calibration applications Wenbo Sun, Bruce Wielicki, Constantine Lukashin, and David Young • Introduction • Polarization fundamentals • Correction of measurement errors caused by polarization • The polarized radiative transfer model • Modeling polarized radiation for clear ocean • Modeling polarized radiation for clouds • Summary
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Modeling polarized radiation for CLARREO inter-calibration applications
Wenbo Sun, Bruce Wielicki, Constantine Lukashin, and David Young
• Introduction
• Polarization fundamentals
• Correction of measurement errors caused by polarization
• The polarized radiative transfer model
• Modeling polarized radiation for clear ocean
• Modeling polarized radiation for clouds
• Summary
Introduction
1. Radiation climatology requires highly accurate radiation data.
2. Instruments whose sensors are not totally depolarized may have
significant errors in measured radiance due to the polarized
incident radiation.
3. Accurate inter-calibration of CLARREO and other instruments
requires the measurement errors due to polarization to be
corrected in advance.
4. Satellite measurements of the polarization of radiation are limited
by incidence and viewing geometries and working wavelengths.
5. To make high-spectral lookup tables of polarization dependence
model (PDM), modeling of the polarization of radiation is needed.
Any arbitrarily polarized incoherent radiation can be represented by
the linear sum of an unpolarized part and a 100% polarized part as
V
U
Q
VUQVUQI
V
U
Q
I 222222
0
0
0
IDOPVUQI pol 222
IDOPVUQIIunpol )1(222
IIDOP polI
VUQ/
222
Q
U)2tan(
Polarization fundamentals
Angle of linear polarization (ALP) physically is
the angle between direction and the linearly
polarized electric field vector. Zero-ALP is
always along the local meridian line. 90-degree-
ALP is ensured at a direction horizontal to the
reflecting surface on the principal plane.
Sensor
e
//e
e
*
////
* EEEEQ
*
////
* EEEEI
*
//
*
// EEEEU
E
Local meridian line
E
IDOPGIDOPGI unpolpolm )1()(
)]1()(/[ DOPGDOPGII unpolpolm
Measured Radiance:
Corrected Radiance:
where )(polG unpolGand
are sensor’s gain factors for linearly polarized radiation and
unpolarized radiation, respectively, which can be measured in lab
using a linearly polarized incidence over the whole concerned
spectrum. The gain factor for unpolarized portion of incidence
can then be derived out as
0
)(1
dGG polunpol
Correction of measurement errors caused
by polarization
1. Adding-Doubling radiative transfer model:This can calculate full Stokes vector (I, Q, U, V). But for CLARREO, I,Q, and U are enough.
2. Atmospheric profiles: Standard Atmosphere now.
3. Spectral gas absorption: Line-by-Line and k-distribution plus ozone cross-section table.
4. Molecular scattering: Rayleigh.
5. Particulate absorption and scattering: Mie for water clouds (Gamma size distribution); FDTD for aerosols (lognormal size distribution with fine and coarse mode);FDTD plus GOM for ice clouds (lognormal or measured size distributions).
6. Surface reflection model: Lambert surface for land now.Cox & Munk + foam for wind-roughened ocean.
The polarized radiative transfer model
0 10 20 30 40 50 60 70 80 90
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
RAZ = 180o
VZA (o)
Re
fle
cta
nce
90 80 70 60 50 40 30 20 10 0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Ocean Wind:
2.5 m/s
5.0 m/s
7.5 m/s
10.0 m/s
15.0 m/s
VZA (o)
WL = 670 nm
SZA = 30o
RAZ = 0o
Re
fle
cta
nce
90 80 70 60 50 40 30 20 10 0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Ocean Wind:
2.5 m/s
5.0 m/s
7.5 m/s
10.0 m/s
15.0 m/s
WL = 670 nm
SZA = 30o
RAZ = 0o
DO
P
VZA (o)
0 10 20 30 40 50 60 70 80 90
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
RAZ = 180o
DO
P
VZA (o)
Sea-Salt AOT = 0.075
Sensitivity of clear ocean total reflectance and DOP to wind speed
10 20 30 40 50 60
5
10
15
20
25
30
35
Wind = 12.5 m/s
DO
P
RAZ ( x 3o )
VZ
A (
1.9
o...8
8.7
o in
Ga
ussia
n Q
ua
dra
ture
)
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.010 20 30 40 50 60
5
10
15
20
25
30
35
Wind = 7.5 m/s
DO
P
RAZ ( x 3o )
VZ
A (
1.9
o...8
8.7
o in
Ga
ussia
n Q
ua
dra
ture
)
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.010 20 30 40 50 60
5
10
15
20
25
30
35
WL = 670 nm
SZA = 30o
RAZ = 0o
Wind = 2.5 m/s
DO
PRAZ ( x 3
o )
VZ
A (
1.9
o...8
8.7
o in
Ga
ussia
n Q
ua
dra
ture
)
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
10 20 30 40 50 60
5
10
15
20
25
30
35
Wind = 2.5 m/s
WL = 670 nm
SZA = 30o
RAZ = 0o
AL
P
RAZ ( x 3o )
VZ
A (
1.9
o...8
8.7
o in
Ga
ussia
n Q
ua
dra
ture
)
0
15
30
45
60
75
90
105
120
135
150
165
18010 20 30 40 50 60
5
10
15
20
25
30
35
AL
P
Wind = 7.5 m/s
RAZ ( x 3o )
VZ
A (
1.9
o...8
8.7
o in
Ga
ussia
n Q
ua
dra
ture
)
0
15
30
45
60
75
90
105
120
135
150
165
18010 20 30 40 50 60
5
10
15
20
25
30
35
Wind = 12.5 m/s
AL
P
RAZ ( x 3o )
VZ
A (
1.9
o...8
8.7
o in
Ga
ussia
n Q
ua
dra
ture
)
0
15
30
45
60
75
90
105
120
135
150
165
180
(Sea-salt AOT = 0.075)
Wind = 2.5 m/s Wind = 7.5 m/s Wind = 12.5 m/s
Sensitivity of clear ocean DOP and ALP to wind
speed
90 80 70 60 50 40 30 20 10 0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
AOT = 0.00
AOT = 0.075
AOT = 0.075 x 2
WL = 670 nm
SZA = 30o
RAZ = 0o
Wind = 7.5 m/s
DO
P
VZA (o)
0 10 20 30 40 50 60 70 80 90
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
RAZ = 180o
DO
P
VZA (o)
Sensitivity of clear ocean DOP and ALP to aerosol
90 80 70 60 50 40 30 20 10 0
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
AOT = 0.00
AOT = 0.075
AOT = 0.075 x 2
WL = 670 nm
SZA = 30o
RAZ = 0o
Wind = 7.5 m/s
VZA ( o )
Re
fle
cta
nce
0 10 20 30 40 50 60 70 80 90
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
Re
fle
cta
nce
RAZ = 180o
VZA ( o )
90 80 70 60 50 40 30 20 10 0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
SZA = 60o
SZA = 30o
WL = 670 nm
Wind = 7.5 m/s
RAZ = 0o
VZA ( o )
DO
P
0 10 20 30 40 50 60 70 80 90
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
RAZ = 180o
DO
P
VZA ( o )
Sensitivity of clear ocean total reflectance and DOP to solar zenith angle
90 80 70 60 50 40 30 20 10 0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
SZA = 60o
SZA = 30o
WL = 670 nm
Wind = 7.5 m/s
RAZ = 0o
Re
fle
cta
nce
VZA (o)
0 10 20 30 40 50 60 70 80 90
0.0
0.5
1.0
1.5
2.0
2.5
3.0
RAZ = 180o
VZA (o)
Re
fle
cta
nce
DO
P
SZA = 60o
WL = 670 nm
Wind = 7.5 m/s
AOT = 0.075
X Axis Title
Y A
xis
Title
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Sensitivity of clear ocean DOP to solar
zenith angle
SZA = 30o
WL = 670 nm
Wind = 7.5 m/s
AOT = 0.075
DO
P
X Axis Title
Y A
xis
Title
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Radiance in the blue
angle range has ~0
degree of polarization.
These neutral-
polarization VZAs are
suitable for calibrating
polarized sensors such
as the instruments on
PARASOL or Glory.
0 10 20 30 40 50 60 70 80 90
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
RAZ = 180o
DO
P
VZA (o)
90 80 70 60 50 40 30 20 10 0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
WL = 670 nm
WL = 865 nm
Ocean Wind = 7.5 m/s
SZA = 30o
RAZ = 0o
DO
P
VZA (o)
Sensitivity of clear ocean total reflectance and DOP to wavelength