The authors are with the Atmospheric Radiation and Satellite Remote Sensing Laboratory, Chengdu Meteorological College, Chengdu, Sichuan 610041, China.
Lisheng Xu and Jianyun Zhang, "Simulation study of the remote sensing of optical and microphysical properties of cirrus clouds from satellite IR measurements," Appl. Opt. 34, 2724-2736 (1995)
Improved ray-optics theory and Mie theory for single scattering and an adding–doubling method for multiple scattering have been used to study the interaction of radiation in NASA’s Visible and Infrared Spin-Scan Radiometer Atmospheric Sounder Satellite (VAS) IR channels and the microphysics of inhomogeneous cirrus clouds. The simulation study shows that crystal shape has remarkable effects on scattering and on the radiative-transfer properties of cirrus clouds in IR spectra. The sensitivity of the brightness temperature, as observed with VAS-IR channels, to the hexagonal columns and plates in cirrus clouds is noticeable. A method that permits one to infer the optical thickness, crystal shape, ice–water content, and emittance of cirrus clouds by using a multi-IR window channel with a scanning observation technique is developed. Detailed error analyses are carried out, and the characteristics of VAS-IR window channels are investigated through the examination of the effects of sea-surface reflection and variations in the temperature and water-vapor profiles on the VAS measurements. It is shown that these effects are large and need to be considered. Some uncertainties that have risen from the theoretical model are studied; they demonstrate that the Mie-scattering theory should not be used to retrieve the microphysical and optical properties of cirrus clouds. A suitable cloud-microphysics model and a suitable scattering model are needed instead.
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N represents the total ice-crystal number density.
Table 2
Fitting Coefficients for the Parameterization of Cirrus-Cloud Optical Thickness as Calculated with Eq. (4)
Shape
Δ BT(j–m)
a0
a1
a2
a3
a4
a5
a6
a7
a8
a9
rms σ
Channel for τc
Column
ΔBT(12–7)
10808.2
−6699.74
1801.02
−275.637
26.4821
−1.65766
6.76693 × 10−2
−1.73909 × 10−3
2.55625 × 10−5
−1.63932 × 10−7
1.14 × 10−1
No. 5
Column
ΔBT(8–5)
−114.882
222.560
−169.853
68.8445
−16.5267
2.46269
−2.29935 × 10−1
1.30767 × 10−2
−4.13916 × 10−4
5.58879 × 10−6
1.99 × 10−1
No. 5
Plate
ΔBT(8–5)
1.84982
−2.47501 × 10−4
1.83013 × 10−1
−9.08558 × 10−2
−1.65710 × 10−2
1.10585 × 10−2
−1.33724 × 10−3
−5.82139 × 10−6
9.39803 × 10−6
−4.12802 × 10−7
1.62 × 10−1
No. 5
Column plus plate
ΔBT(8–5)
1.91474
−1.12644 × 10−1
7.10665 × 10−2
−3.46368 × 10−2
−2.69739 × 10−3
3.23906 × 10−3
−5.95161 × 10−4
4.85326 × 10−5
−1.87112 × 10−6
2.75721 × 10−8
2.47 × 10−1
No. 5
These data were obtained through the use of the numerical-fitting method under the following conditions: Four model atmospheres (i.e., U.S. standard, tropical, midlatitude summer, and midlatitude winter) for cirrus clouds, IWC = 0.02 g m−3, a satellite zenith angle θ that is changing from 0° to 45°, with single-scattering calculations where Lc = 100 μm. The total number of points used to fit the data was N = 32 for each value.
Table 3
Fitting Coefficients for the Parameterization of the IR Emittance of Cirrus Clouds as Represented by the Cloud Optical Thickness Obtained with Eq. (5)a
Shape
b0
b1
b2
b3
b4
b5
b6
rms σ
Channels for ɛc
Column
−9.65252 × 10−3
8.95770 × 10−1
−1.45085
1.79034
−9.99000 × 10−1
2.00375 × 10−1
0.00
3.35 × 10−3
No. 5
Plate
−3.19139 × 10−3
7.61962 × 10−1
−7.29794 × 10−1
5.38851 × 10−1
−1.89273 × 10−1
2.43133 × 10−1
0.00
4.29 × 10−3
No. 5
Column plus plate
−1.39021 × 10−2
9.71477 × 10−1
−1.76336
2.34977
−1.54988
4.80171 × 10−1
−5.60742 × 10−2
6.70 × 10−3
No. 5
These data were obtained through the use of the numerical-fitting method under the following conditions: Four model atmospheres (see footnote a, Table 2), 10−3 < 1 WC < 0.02 g m−3, 0° < θ < 45°, and Lc = 100 μm. The total number of points used to fit the data was N = 64 for each value.
Table 4
Fitting Coefficients for the Parameterization of the IR Emittance of Cirrus Clouds as Represented by the BT Obtained with Eq. (6)a
Shape
C0
C1
C2
C3
C4
C5
rms σ
Channels for ɛc
Column
2.4076 × 10−1
2.43962 × 10−1
−6.23031 × 10−2
5.84334 × 10−3
−2.44739 × 10−4
3.82625 × 10−6
1.003 × 10−2
No. 8
1.60530 × 10−1
1.58696 × 10−1
−4.11947 × 10−2
3.87002 × 10−3
−1.61194 × 10−4
2.49915 × 10−6
6.22 × 10−2
No. 12
Plate
5.13603 × 10−1
−3.44329 × 10−2
2.84174 × 10−3
−6.48049 × 10−4
4.49825 × 10−5
0.00
6.28 × 10−3
No. 12
6.49211 × 10−1
−3.73659 × 10−2
2.91718 × 10−3
−7.87980 × 10−4
5.61335 × 10−5
−1.14393 × 10−6
7.92 × 10−2
No. 6
Column plus plate
5.10234 × 10−1
−4.15463 × 10−2
1.19722 × 10−3
−1.51661 × 10−4
1.16718 × 10−5
−2.41641 × 10−7
6.53 × 10−2
No. 12
These data were obtained under the same conditions that were given in Table 3 (footnote a).
Table 5
Simulation of the Effect of the Sea-Surface Reflection on BT as Measured with VAS-IR Window Channelsa
Particle Shape
σi
Channel 5
Channel 6
Channel 7
Channel 8
Channel 12
Column
0.591
0.037
0.794
1.793
0.347
Plate
0.595
0.037
0.746
1.716
0.338
These data were obtained under the following conditions: A U.S. standard atmosphere, three IWC values for cirrus clouds (IWC = 5 × 10−5, 10−3, 0.02 g m−3), zenith angles θ = 0°, 15°, 30°, 45°, 60°. The total sample number was N = 30.
Table 6
Simulation of the Effect of Variations in Water-Vapor ρH2O and Temperature T(z) Profiles on the BT as Measured with VAS-IR Window Channelsa
Profile
Variation
Particle Shape
σi
Channel 5
Channel 6
Channel 7
Channel 8
Channel 12
ρ H2O(z)
From U.S. to MS
Columns
1.446
0.806
1.417
0.354
0.105
Plates
1.517
0.841
1.481
0.367
0.110
ρ H2O(z)
From U.S. to MW
Columns
0.667
0.305
0.633
0.152
0.096
Plates
0.698
0.319
0.661
0.157
0.100
T(z)
From U.S. to MS
Columns
3.965
3.754
4.042
3.951
3.863
Plates
4.325
4.043
4.411
4.312
4.125
T(z)
From U.S. to MW
Columns
3.662
3.824
5.231
5.857
6.481
Plates
3.851
3.978
5.481
6.130
6.782
Combined T(z) and ρH2O
From U.S. to MS
Columns
2.682
3.432
2.813
3.266
3.770
Plates
3.061
3.717
3.197
3.630
4.028
Combined T(z) and ρH2O
From U.S. to MW
Columns
3.232
3.733
4.843
5.675
6.441
Plates
3.401
3.884
5.076
5.940
6.740
In the numerical simulation, three IWC values (IWC = 5 × 10−5, 10−3, 0.02 g m−3) and five zenith angles (θ = 0°, 15°, 30°, 45°, 60°) were used. The total sample number was N = 30.
Table 7
Error σ of ΔBT(8–5) Caused by Some Important Variationsa
σ denotes the rms error with the temperature measured in kelvins. In the numerical calculations, values of 0° ≤ θ ≤ 45° are assumed. For each value in the table, the total number of points used to fit the data was N = 32.
σ derived from the Mie scattering theory.
σ caused by Lc changing from 100 μm to 70 μm.
Tables (7)
Table 1
Parameter Values for the Calculation of N2(r) in Eq. (2) for α2 = 2
N represents the total ice-crystal number density.
Table 2
Fitting Coefficients for the Parameterization of Cirrus-Cloud Optical Thickness as Calculated with Eq. (4)
Shape
Δ BT(j–m)
a0
a1
a2
a3
a4
a5
a6
a7
a8
a9
rms σ
Channel for τc
Column
ΔBT(12–7)
10808.2
−6699.74
1801.02
−275.637
26.4821
−1.65766
6.76693 × 10−2
−1.73909 × 10−3
2.55625 × 10−5
−1.63932 × 10−7
1.14 × 10−1
No. 5
Column
ΔBT(8–5)
−114.882
222.560
−169.853
68.8445
−16.5267
2.46269
−2.29935 × 10−1
1.30767 × 10−2
−4.13916 × 10−4
5.58879 × 10−6
1.99 × 10−1
No. 5
Plate
ΔBT(8–5)
1.84982
−2.47501 × 10−4
1.83013 × 10−1
−9.08558 × 10−2
−1.65710 × 10−2
1.10585 × 10−2
−1.33724 × 10−3
−5.82139 × 10−6
9.39803 × 10−6
−4.12802 × 10−7
1.62 × 10−1
No. 5
Column plus plate
ΔBT(8–5)
1.91474
−1.12644 × 10−1
7.10665 × 10−2
−3.46368 × 10−2
−2.69739 × 10−3
3.23906 × 10−3
−5.95161 × 10−4
4.85326 × 10−5
−1.87112 × 10−6
2.75721 × 10−8
2.47 × 10−1
No. 5
These data were obtained through the use of the numerical-fitting method under the following conditions: Four model atmospheres (i.e., U.S. standard, tropical, midlatitude summer, and midlatitude winter) for cirrus clouds, IWC = 0.02 g m−3, a satellite zenith angle θ that is changing from 0° to 45°, with single-scattering calculations where Lc = 100 μm. The total number of points used to fit the data was N = 32 for each value.
Table 3
Fitting Coefficients for the Parameterization of the IR Emittance of Cirrus Clouds as Represented by the Cloud Optical Thickness Obtained with Eq. (5)a
Shape
b0
b1
b2
b3
b4
b5
b6
rms σ
Channels for ɛc
Column
−9.65252 × 10−3
8.95770 × 10−1
−1.45085
1.79034
−9.99000 × 10−1
2.00375 × 10−1
0.00
3.35 × 10−3
No. 5
Plate
−3.19139 × 10−3
7.61962 × 10−1
−7.29794 × 10−1
5.38851 × 10−1
−1.89273 × 10−1
2.43133 × 10−1
0.00
4.29 × 10−3
No. 5
Column plus plate
−1.39021 × 10−2
9.71477 × 10−1
−1.76336
2.34977
−1.54988
4.80171 × 10−1
−5.60742 × 10−2
6.70 × 10−3
No. 5
These data were obtained through the use of the numerical-fitting method under the following conditions: Four model atmospheres (see footnote a, Table 2), 10−3 < 1 WC < 0.02 g m−3, 0° < θ < 45°, and Lc = 100 μm. The total number of points used to fit the data was N = 64 for each value.
Table 4
Fitting Coefficients for the Parameterization of the IR Emittance of Cirrus Clouds as Represented by the BT Obtained with Eq. (6)a
Shape
C0
C1
C2
C3
C4
C5
rms σ
Channels for ɛc
Column
2.4076 × 10−1
2.43962 × 10−1
−6.23031 × 10−2
5.84334 × 10−3
−2.44739 × 10−4
3.82625 × 10−6
1.003 × 10−2
No. 8
1.60530 × 10−1
1.58696 × 10−1
−4.11947 × 10−2
3.87002 × 10−3
−1.61194 × 10−4
2.49915 × 10−6
6.22 × 10−2
No. 12
Plate
5.13603 × 10−1
−3.44329 × 10−2
2.84174 × 10−3
−6.48049 × 10−4
4.49825 × 10−5
0.00
6.28 × 10−3
No. 12
6.49211 × 10−1
−3.73659 × 10−2
2.91718 × 10−3
−7.87980 × 10−4
5.61335 × 10−5
−1.14393 × 10−6
7.92 × 10−2
No. 6
Column plus plate
5.10234 × 10−1
−4.15463 × 10−2
1.19722 × 10−3
−1.51661 × 10−4
1.16718 × 10−5
−2.41641 × 10−7
6.53 × 10−2
No. 12
These data were obtained under the same conditions that were given in Table 3 (footnote a).
Table 5
Simulation of the Effect of the Sea-Surface Reflection on BT as Measured with VAS-IR Window Channelsa
Particle Shape
σi
Channel 5
Channel 6
Channel 7
Channel 8
Channel 12
Column
0.591
0.037
0.794
1.793
0.347
Plate
0.595
0.037
0.746
1.716
0.338
These data were obtained under the following conditions: A U.S. standard atmosphere, three IWC values for cirrus clouds (IWC = 5 × 10−5, 10−3, 0.02 g m−3), zenith angles θ = 0°, 15°, 30°, 45°, 60°. The total sample number was N = 30.
Table 6
Simulation of the Effect of Variations in Water-Vapor ρH2O and Temperature T(z) Profiles on the BT as Measured with VAS-IR Window Channelsa
Profile
Variation
Particle Shape
σi
Channel 5
Channel 6
Channel 7
Channel 8
Channel 12
ρ H2O(z)
From U.S. to MS
Columns
1.446
0.806
1.417
0.354
0.105
Plates
1.517
0.841
1.481
0.367
0.110
ρ H2O(z)
From U.S. to MW
Columns
0.667
0.305
0.633
0.152
0.096
Plates
0.698
0.319
0.661
0.157
0.100
T(z)
From U.S. to MS
Columns
3.965
3.754
4.042
3.951
3.863
Plates
4.325
4.043
4.411
4.312
4.125
T(z)
From U.S. to MW
Columns
3.662
3.824
5.231
5.857
6.481
Plates
3.851
3.978
5.481
6.130
6.782
Combined T(z) and ρH2O
From U.S. to MS
Columns
2.682
3.432
2.813
3.266
3.770
Plates
3.061
3.717
3.197
3.630
4.028
Combined T(z) and ρH2O
From U.S. to MW
Columns
3.232
3.733
4.843
5.675
6.441
Plates
3.401
3.884
5.076
5.940
6.740
In the numerical simulation, three IWC values (IWC = 5 × 10−5, 10−3, 0.02 g m−3) and five zenith angles (θ = 0°, 15°, 30°, 45°, 60°) were used. The total sample number was N = 30.
Table 7
Error σ of ΔBT(8–5) Caused by Some Important Variationsa
σ denotes the rms error with the temperature measured in kelvins. In the numerical calculations, values of 0° ≤ θ ≤ 45° are assumed. For each value in the table, the total number of points used to fit the data was N = 32.
σ derived from the Mie scattering theory.
σ caused by Lc changing from 100 μm to 70 μm.