Eyk Boesche,1,2
Piet Stammes,
Thomas Ruhtz,1
Réne Preusker,
and Juergen Fischer1
1When this research was performed, E. Boesche (boesche@wew.fu-berlin.de), T. Ruhtz, R. Preusker, and J. Fischer were with the Institute for Space Sciences, Free University Berlin, Carl-Heinrich-Becker-Weg 6-10, 12165 Berlin, Germany.
2E. Boesche is currently working with P. Stammes (stammes@knmi.nl) at the Royal Netherlands Meteorological Institute, P. O. Box 201, 2730 AE de Bilt, The Netherlands.
Eyk Boesche, Piet Stammes, Thomas Ruhtz, Réne Preusker, and Juergen Fischer, "Effect of aerosol microphysical properties on polarization of skylight: sensitivity study and measurements," Appl. Opt. 45, 8790-8805 (2006)
We analyze the sensitivity of the degree of linear polarization in the Sun's principal plane as a function of aerosol microphysical parameters: the real and imaginary parts of the refractive index, the median radius and geometric standard deviation of the bimodal size distribution
(both fine and coarse modes), and the relative number weight of the fine mode at a wavelength of
. We use Mie theory for single-scattering simulations and the
doubling–adding method with the inclusion of polarization for multiple scattering. It is shown that the behavior of the degree of linear polarization is highly sensitive to both the small mode of the bimodal size distribution and the real part of the refractive index of aerosols, as well as to the aerosol optical thickness; whereas not all parameters influence the polarization equally.
A classification of the importance of the input parameters is given. This sensitivity study is applied to an analysis of ground-based polarization measurements. For the passive remote sensing of microphysical and optical properties of aerosols, a ground-based spectral polarization measuring system was built, which aims to measure the Stokes parameters I, Q,
and U in the visible (from 410 to
) and near-infrared (from 674 to
) spectral range with a spectral resolution of
in the visible and
in the near infrared. We compare polarization measurements taken with radiative transfer simulations under both clear- and hazy-sky conditions in an urban area (Cabauw, The Netherlands,
,
).
Conclusions about the microphysical properties of aerosol are drawn from the comparison.
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The Cabauw values are used as standard input for the Mie simulations. The fourth column gives the range in which the values are varied for the sensitivity study. For comparison purposes the fifth and sixth columns give the average values as measured by AERONET in urban locations (Greenbelt and Paris).[11]
Table 2
Input Parameters for the DAK Multiple Scattering Simulationsa
DAK Input Parameter
Symbol
Standard Value (Cabauw, The Netherlands)
Range
Wavelength
λ (μm)
0.675
Constant
Surface albedo
A
0.10
0.05–0.20
Atmospheric profile
Mid-latitude Summer,AFGL (1986)
—
Number of atmospheric layers
N
32
Constant
Aerosol altitude
h (km)
0–1
0–16
Mie input parameters
See Table 1
—
Aerosol optical thickness
0.065
0.045–0.400
The third column gives the standard Cabauw case values for 11 October 2004. The fourth column gives the range in which the parameters are varied in the sensitivity study.
Table 3
Summary of the Aerosol Model Parameters for Clear (11 October 2004) and Hazy (8 May 2003) Sky Conditions
Parameter
Symbol
Cabauw Standard Case
Best Fit for 11 October 2004
Best Fit for 8 May 2003
Aerosol microphysical parameters (Mie)
Wavelength
λ (μm)
0.675
0.675
0.675
Imaginary part of the refractive index
mi
0.007
0.0007
0.0000
Real part of the refractive index
mr
1.400
1.400
1.380
Median radius of the fine mode
rf (μm)
0.080
0.080
0.120
Median radius of the coarse mode
rc (μm)
0.425
0.425
0.700
Standard deviation of the fine mode
σf
1.400
1.300
1.950
Standard deviation of the coarse mode
σc
2.200
2.200
2.200
Weighting factor of the fine mode
w
0.9995
0.9996
0.9992
Average volume
V
0.0055
0.0069
0.0725
Average volume fine mode
Vf
0.0036
0.0029
0.0538
Macrophysical parameters (DAK)
Aerosol altitude
h (km)
1
1
1
Aerosol optical thickness
0.065
0.065
0.390
Surface albedo
A
0.10
0.10
0.15
Mean deviation of the degree of polarization(fit measurement)
(%)
1.49
0.30
−0.811
RMSE of the degree of polarization (fit measurement)
(%)
1.35
0.76
0.91
Single-scattering albedo
ω
0.887
0.977
1.000
Fine mode fraction of
(%)
70
51
17
Table 4
Classification of the Importance of the DAK and Mie Input Parametersa
Parameters
Forward Polarization
Maximum Polarization
Position of Maximum
Backward Polarization
Clear
Hazy
Clear
Hazy
Clear
Hazy
Clear
Hazy
Microphysical aerosol parameters (Mie)
Imaginary part of the refractive index
mi
−
+
−
+
−−
−−
−−
+
Real part of the refractive index
mr
+
++
+
++
−
+
−−
++
Median radius of the fine mode
rf
++
++
++
++
−−
−
+
+
Median radius of the coarse mode
rc
−
−−
−
−−
−
−−
−−
−−
Standard deviation of the fine mode
σf
++
++
++
++
+
++
+
+
Standard deviation of the coarse mode
σc
−−
−−
−−
−−
−−
−−
−−
−−
Weighting factor of the fine mode
w
+
−−
+
−−
−
−−
−
−−
Macrophysical parameters (DAK)
Aerosol altitude
h
−−
−−
−−
−−
−−
−−
−−
−−
Aerosol optical thickness
+
++
++
++
−−
−−
++
++
Surface albedo
A
−−
−−
+
−
−−
−−
−
−
The classification is for multiple scattering simulations (column 1) and their effects on the degree of linear polarization in the forward-scattering direction (column 2), the maximum polarization (column 3), the position of the maximum (column 4), and the polarization in the backscattering direction (column 5). Two sky cases are considered: clear sky (11 October 2004, Table 3) and hazy sky (8 May 2003, Table 3). Classification of the effects is as follows: very significant (++), significant (+), minor (−), and insignificant (−−) (see Subsection 3.D).
Table 5
Technical Data of the FUBISS–POLAR Polarization Spectrometer
The Cabauw values are used as standard input for the Mie simulations. The fourth column gives the range in which the values are varied for the sensitivity study. For comparison purposes the fifth and sixth columns give the average values as measured by AERONET in urban locations (Greenbelt and Paris).[11]
Table 2
Input Parameters for the DAK Multiple Scattering Simulationsa
DAK Input Parameter
Symbol
Standard Value (Cabauw, The Netherlands)
Range
Wavelength
λ (μm)
0.675
Constant
Surface albedo
A
0.10
0.05–0.20
Atmospheric profile
Mid-latitude Summer,AFGL (1986)
—
Number of atmospheric layers
N
32
Constant
Aerosol altitude
h (km)
0–1
0–16
Mie input parameters
See Table 1
—
Aerosol optical thickness
0.065
0.045–0.400
The third column gives the standard Cabauw case values for 11 October 2004. The fourth column gives the range in which the parameters are varied in the sensitivity study.
Table 3
Summary of the Aerosol Model Parameters for Clear (11 October 2004) and Hazy (8 May 2003) Sky Conditions
Parameter
Symbol
Cabauw Standard Case
Best Fit for 11 October 2004
Best Fit for 8 May 2003
Aerosol microphysical parameters (Mie)
Wavelength
λ (μm)
0.675
0.675
0.675
Imaginary part of the refractive index
mi
0.007
0.0007
0.0000
Real part of the refractive index
mr
1.400
1.400
1.380
Median radius of the fine mode
rf (μm)
0.080
0.080
0.120
Median radius of the coarse mode
rc (μm)
0.425
0.425
0.700
Standard deviation of the fine mode
σf
1.400
1.300
1.950
Standard deviation of the coarse mode
σc
2.200
2.200
2.200
Weighting factor of the fine mode
w
0.9995
0.9996
0.9992
Average volume
V
0.0055
0.0069
0.0725
Average volume fine mode
Vf
0.0036
0.0029
0.0538
Macrophysical parameters (DAK)
Aerosol altitude
h (km)
1
1
1
Aerosol optical thickness
0.065
0.065
0.390
Surface albedo
A
0.10
0.10
0.15
Mean deviation of the degree of polarization(fit measurement)
(%)
1.49
0.30
−0.811
RMSE of the degree of polarization (fit measurement)
(%)
1.35
0.76
0.91
Single-scattering albedo
ω
0.887
0.977
1.000
Fine mode fraction of
(%)
70
51
17
Table 4
Classification of the Importance of the DAK and Mie Input Parametersa
Parameters
Forward Polarization
Maximum Polarization
Position of Maximum
Backward Polarization
Clear
Hazy
Clear
Hazy
Clear
Hazy
Clear
Hazy
Microphysical aerosol parameters (Mie)
Imaginary part of the refractive index
mi
−
+
−
+
−−
−−
−−
+
Real part of the refractive index
mr
+
++
+
++
−
+
−−
++
Median radius of the fine mode
rf
++
++
++
++
−−
−
+
+
Median radius of the coarse mode
rc
−
−−
−
−−
−
−−
−−
−−
Standard deviation of the fine mode
σf
++
++
++
++
+
++
+
+
Standard deviation of the coarse mode
σc
−−
−−
−−
−−
−−
−−
−−
−−
Weighting factor of the fine mode
w
+
−−
+
−−
−
−−
−
−−
Macrophysical parameters (DAK)
Aerosol altitude
h
−−
−−
−−
−−
−−
−−
−−
−−
Aerosol optical thickness
+
++
++
++
−−
−−
++
++
Surface albedo
A
−−
−−
+
−
−−
−−
−
−
The classification is for multiple scattering simulations (column 1) and their effects on the degree of linear polarization in the forward-scattering direction (column 2), the maximum polarization (column 3), the position of the maximum (column 4), and the polarization in the backscattering direction (column 5). Two sky cases are considered: clear sky (11 October 2004, Table 3) and hazy sky (8 May 2003, Table 3). Classification of the effects is as follows: very significant (++), significant (+), minor (−), and insignificant (−−) (see Subsection 3.D).
Table 5
Technical Data of the FUBISS–POLAR Polarization Spectrometer
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