Lisheng Xu and Jianyun Zhang, "Simulation of retrieval of the base height and thickness of cirrus clouds from satellite data," J. Opt. Soc. Am. A 9, 1536-1546 (1992)
On the basis of the theory of scattering and radiative transfer in atmospheres with cirrus clouds, a physical retrieval method for the base height and thickness of cirrus clouds is developed in this simulation study. A complicated nonlinear equation is derived and solved, the radiative properties of cirrus clouds are parameterized, and the transmittance profile in atmospheres with cirrus clouds is developed. Two numerical techniques, Müller iteration and a Monte Carlo method, are used. Retrieval results are presented for various atmospheric models and ice-water contents. Detailed analyses of observation errors and theoretical model errors, especially for the cloud microphysics, are carried out. Our analyses of the sensitivity of the method to ice-water content include vertical homogeneities and inhomogeneities. The preliminary study shows that the method developed here is feasible and that the VAS satellite’s IR channels 7 (12-μm H2O window) and 8 (11-μm atmospheric window) are important and useful for passive remote sensing of atmospheres with cirrus clouds from satellites.
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, where δ is the optical thickness of the cirrus clouds; θ = 0°.
1 denotes the U.S. standard atmosphere, and 2 denotes tropical.
Based on IWC. I includes 5 × 10−5 ≤ IWC 10−3 gm−3, II includes 10−3 ≤ IWC ≤ 0.02 gm−3, and III includes 0.02 ≤ IWC ≤ 0.25 gm−3.
, where δ is the optical thickness of the cirrus clouds; θ = 0°.
1 denotes the U.S. standard atmosphere, and 2 denotes tropical.
Based on IWC. I includes 5 × 10−5 ≤ IWC ≤ 10−3 gm−3, II includes 10−3 IWC ≤ 0.02 gm−3, and III includes 0.02 ≤ IWC ≤ 0.25 gm−1.
1 denotes U.S. standard atmosphere, and 2 denotes tropical.
Index of IWC: 1, 2, 3, and 4 denote 5 × 10−5, 10−3, 0.02, and 0.25 gm−3, respectively.
Ray-optics computations; θ = 0°.
Error values are calculated for data for four atmospheric models, N = 31.
Table 4
Cloud Thickness Retrieval Error σ Caused by Variations in Cloud-Top Heighta
Lower Layer: 1.8 × IWC, Particle-Size Range 5–1500 μm
7
2
0.93
0.05016
0.04590
0.524
0.517
0.03017
0.02760
3
0.8205
0.7648
0.541
0.530
0.4935
0.4600
8
2
0.96
0.04889
0.04486
0.527
0.521
0.02940
0.02698
3
0.7983
0.7468
0.526
0.514
0.4801
0.4491
Upper Layer: 0.2 × IWC, Particle-Size Range 1–550 μm
7
2
0.92
0.002700
0.002882
0.319
0.326
0.001624
0.001733
3
0.03939
0.04177
0.502
0.500
0.02369
0.02512
8
2
0.95
0.002581
0.002744
0.507
0.504
0.001553
0.001650
3
0.03733
0.03937
0.507
0.503
0.02245
0.02368
U.S. standard atmosphere; reL ≈ reU.
Index of IWC: 2 and 3 denote 10−3 and 0.02 gm−3, respectively.
Asymmetry factor.
Ray-optics computations.
Table 7
Optical Thicknesses δ for Vertically Homogeneous and Inhomogeneous Cirrus Clouds as Calculated by Mie Scattering Theory (MST) and Ray-Optics Theory (ROT) for a Hexagonal Columna
Statistics are calculated for data in two atmospheric models: U.S. standard atmosphere and tropical, N = 15.
Type 1 two-layer ice model. IWC: lower, 1.8 IWC; upper, 0.2 IWC.
Type 2 two-layer ice model. IWC: lower, 1.2 IWC; upper, 0.8 IWC.
, where δ is the optical thickness of the cirrus clouds; θ = 0°.
1 denotes the U.S. standard atmosphere, and 2 denotes tropical.
Based on IWC. I includes 5 × 10−5 ≤ IWC 10−3 gm−3, II includes 10−3 ≤ IWC ≤ 0.02 gm−3, and III includes 0.02 ≤ IWC ≤ 0.25 gm−3.
, where δ is the optical thickness of the cirrus clouds; θ = 0°.
1 denotes the U.S. standard atmosphere, and 2 denotes tropical.
Based on IWC. I includes 5 × 10−5 ≤ IWC ≤ 10−3 gm−3, II includes 10−3 IWC ≤ 0.02 gm−3, and III includes 0.02 ≤ IWC ≤ 0.25 gm−1.
1 denotes U.S. standard atmosphere, and 2 denotes tropical.
Index of IWC: 1, 2, 3, and 4 denote 5 × 10−5, 10−3, 0.02, and 0.25 gm−3, respectively.
Ray-optics computations; θ = 0°.
Error values are calculated for data for four atmospheric models, N = 31.
Table 4
Cloud Thickness Retrieval Error σ Caused by Variations in Cloud-Top Heighta
Lower Layer: 1.8 × IWC, Particle-Size Range 5–1500 μm
7
2
0.93
0.05016
0.04590
0.524
0.517
0.03017
0.02760
3
0.8205
0.7648
0.541
0.530
0.4935
0.4600
8
2
0.96
0.04889
0.04486
0.527
0.521
0.02940
0.02698
3
0.7983
0.7468
0.526
0.514
0.4801
0.4491
Upper Layer: 0.2 × IWC, Particle-Size Range 1–550 μm
7
2
0.92
0.002700
0.002882
0.319
0.326
0.001624
0.001733
3
0.03939
0.04177
0.502
0.500
0.02369
0.02512
8
2
0.95
0.002581
0.002744
0.507
0.504
0.001553
0.001650
3
0.03733
0.03937
0.507
0.503
0.02245
0.02368
U.S. standard atmosphere; reL ≈ reU.
Index of IWC: 2 and 3 denote 10−3 and 0.02 gm−3, respectively.
Asymmetry factor.
Ray-optics computations.
Table 7
Optical Thicknesses δ for Vertically Homogeneous and Inhomogeneous Cirrus Clouds as Calculated by Mie Scattering Theory (MST) and Ray-Optics Theory (ROT) for a Hexagonal Columna
Statistics are calculated for data in two atmospheric models: U.S. standard atmosphere and tropical, N = 15.
Type 1 two-layer ice model. IWC: lower, 1.8 IWC; upper, 0.2 IWC.
Type 2 two-layer ice model. IWC: lower, 1.2 IWC; upper, 0.8 IWC.
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