A backward Monte Carlo computation procedure has been used to simulate the intensity and degree of polarization of the twilight sky during 1977. It was found that the single scattering approximation is applicable for detection of stratospheric aerosols by twilight measurement during background periods. Based on the simulation, a scheme is proposed for retrieving the stratospheric aerosol scattering coefficient utilizing the measured degree of polarization at the 0.7-μm wavelength in the zenith direction of the twilight sky. Compared with the in situ measurement, both the retrieved total optical depth and the retrieved profile of the aerosol scattering coefficient below 30 km agree reasonably well with measurements.
You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.
You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.
You do not have subscription access to this journal. Article tables are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.
You do not have subscription access to this journal. Equations are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.
Ratio of the Scattered Intensities of Various Orders to First-Order Scattering for Profile A
θ(°)
θ′(°)
2/1
3/1
4/1
5/1
6/1
86.0
86.0
0.090
0.031
0.008
0.002
0.000
88.0
88.0
0.074
0.027
0.005
0.001
0.000
90.0
90.0
0.051
0.018
0.002
0.000
0.000
92.6
91.9
0.015
0.006
0.002
0.000
0.000
93.9
93.0
0.017
0.002
0.002
0.000
0.000
95.3
94.3
0.019
0.001
—
—
—
95.9
95.0
0.031
0.000
—
—
—
Note: The total optical depth above the sea surface level is τ = 0.210 and above the observatory τ′ = 0.0425. θ and θ′ are the true and apparent zenith angles of the sun, respectively. The detecting zenith angle is 0°, and the wavelength is 0.7 μm.
Table II
Ratio of the Scattered Intensities of Various Orders to First-Order Scattering for Profile Ba
θ(°)
θ(°)
2/1
3/1
4/1
5/1
6/1
86.0
86.0
0.092
0.026
0.007
0.001
0.000
88.0
88.0
0.076
0.020
0.005
0.001
0.000
90.0
90.0
0.051
0.012
0.002
0.001
0.000
92.6
91.9
0.030
0.014
0.000
0.000
0.000
93.9
93.0
0.033
0.016
0.001
0.000
0.000
95.3
94.3
0.044
0.009
0.000
0.000
0.000
See footnote to Table I. Here τ = 0.215 and τ′ = 0.0482.
Table III
Comparison of Calculated Intensity I and Polarization δ for Single Scattering Model with those for Monte Carlo Simulation Using the Iterated Aerosol Profile; Optical Depth τ′ = 0.0513
I(×10−2)
δ
θ(°)
M − C
Single
M − C
Single
88.0
0.13
0.10
0.79
0.85
90.0
0.089
0.075
0.82
0.86
92.0
0.038
0.035
0.84
0.85
94.0
0.007
0.006
0.76
0.77
Table IV
Relationship of Solar Zenith Angle with Height of the Contributing Region for the Degree of Polarization
θ(°)
91.0
92.0
92.5
93.0
93.5
94.0
94.5
Height (km)
10.0
13.0
16.0
19.0
21.0
22.0
24.0
Table V
Iterated Results and Errors
Cases
τ′
τm
τa
τa1
Max(δ′/δ0) (%)
δrms
Haze H
0.0513
0.0369
0.0198
0.00894
1.80
0.013
Haze M
0.0482
0.0369
0.0167
0.00591
0.39
0.012
First guess
0.0425
0.0369
0.0110
0.00065
—
—
Note: τ′, τm, τa, and τa1 are the total optical depth above the observatory, the molecular optical depth above the sea surface level the aerosol optical depth above the observatory, and the aerosol optical depth above 11 km, respectively. δ′ is the difference between the observed degree of polarization δ0 and that derived from the iterated aerosol profiles.
Table VI
Results by Using Single Scattering Model
I(×10−2)
δ
θ(°)
Haze H
Haze M
Haze H
Haze M
86.0
0.12
0.12
0.87
0.83
88.0
0.10
0.10
0.88
0.84
90.0
0.077
0.077
0.89
0.85
91.0
0.060
0.060
0.90
0.86
92.0
0.036
0.036
0.89
0.85
92.5
0.027
0.026
0.88
0.83
93.0
0.018
0.018
0.84
0.78
93.5
0.012
0.011
0.81
0.73
94.0
0.0066
0.0065
0.78
0.70
94.5
0.0036
0.0035
0.79
0.72
95.0
0.0015
0.0015
0.85
0.79
96.0
0.00019
0.00019
0.98
0.98
Table VII
Effect of Upper and Lower Atmosphere on Intensity I and Polarization δ; Subscript a refers to Case (a) etc.
θ(°)
Ia(× 10−2)
Ib(× 10−2)
Ic(× 10−2)
δa
δb
δc
88.0
0.40
0.59
0.44
0.79
0.48
0.43
90.0
0.28
0.30
0.23
0.82
0.58
0.44
92.0
0.12
0.12
0.086
0.84
0.60
0.46
94.0
0.022
0.017
0.018
0.76
0.60
0.44
Tables (7)
Table I
Ratio of the Scattered Intensities of Various Orders to First-Order Scattering for Profile A
θ(°)
θ′(°)
2/1
3/1
4/1
5/1
6/1
86.0
86.0
0.090
0.031
0.008
0.002
0.000
88.0
88.0
0.074
0.027
0.005
0.001
0.000
90.0
90.0
0.051
0.018
0.002
0.000
0.000
92.6
91.9
0.015
0.006
0.002
0.000
0.000
93.9
93.0
0.017
0.002
0.002
0.000
0.000
95.3
94.3
0.019
0.001
—
—
—
95.9
95.0
0.031
0.000
—
—
—
Note: The total optical depth above the sea surface level is τ = 0.210 and above the observatory τ′ = 0.0425. θ and θ′ are the true and apparent zenith angles of the sun, respectively. The detecting zenith angle is 0°, and the wavelength is 0.7 μm.
Table II
Ratio of the Scattered Intensities of Various Orders to First-Order Scattering for Profile Ba
θ(°)
θ(°)
2/1
3/1
4/1
5/1
6/1
86.0
86.0
0.092
0.026
0.007
0.001
0.000
88.0
88.0
0.076
0.020
0.005
0.001
0.000
90.0
90.0
0.051
0.012
0.002
0.001
0.000
92.6
91.9
0.030
0.014
0.000
0.000
0.000
93.9
93.0
0.033
0.016
0.001
0.000
0.000
95.3
94.3
0.044
0.009
0.000
0.000
0.000
See footnote to Table I. Here τ = 0.215 and τ′ = 0.0482.
Table III
Comparison of Calculated Intensity I and Polarization δ for Single Scattering Model with those for Monte Carlo Simulation Using the Iterated Aerosol Profile; Optical Depth τ′ = 0.0513
I(×10−2)
δ
θ(°)
M − C
Single
M − C
Single
88.0
0.13
0.10
0.79
0.85
90.0
0.089
0.075
0.82
0.86
92.0
0.038
0.035
0.84
0.85
94.0
0.007
0.006
0.76
0.77
Table IV
Relationship of Solar Zenith Angle with Height of the Contributing Region for the Degree of Polarization
θ(°)
91.0
92.0
92.5
93.0
93.5
94.0
94.5
Height (km)
10.0
13.0
16.0
19.0
21.0
22.0
24.0
Table V
Iterated Results and Errors
Cases
τ′
τm
τa
τa1
Max(δ′/δ0) (%)
δrms
Haze H
0.0513
0.0369
0.0198
0.00894
1.80
0.013
Haze M
0.0482
0.0369
0.0167
0.00591
0.39
0.012
First guess
0.0425
0.0369
0.0110
0.00065
—
—
Note: τ′, τm, τa, and τa1 are the total optical depth above the observatory, the molecular optical depth above the sea surface level the aerosol optical depth above the observatory, and the aerosol optical depth above 11 km, respectively. δ′ is the difference between the observed degree of polarization δ0 and that derived from the iterated aerosol profiles.
Table VI
Results by Using Single Scattering Model
I(×10−2)
δ
θ(°)
Haze H
Haze M
Haze H
Haze M
86.0
0.12
0.12
0.87
0.83
88.0
0.10
0.10
0.88
0.84
90.0
0.077
0.077
0.89
0.85
91.0
0.060
0.060
0.90
0.86
92.0
0.036
0.036
0.89
0.85
92.5
0.027
0.026
0.88
0.83
93.0
0.018
0.018
0.84
0.78
93.5
0.012
0.011
0.81
0.73
94.0
0.0066
0.0065
0.78
0.70
94.5
0.0036
0.0035
0.79
0.72
95.0
0.0015
0.0015
0.85
0.79
96.0
0.00019
0.00019
0.98
0.98
Table VII
Effect of Upper and Lower Atmosphere on Intensity I and Polarization δ; Subscript a refers to Case (a) etc.
Add to BibSonomy