Multiple-Scattering Approximation Model Among Horizontally Adjacent Fields for Three-Dimensional Radiative Transfer in Cloud Remote Sensing

Yin Zhang; Hao Yan; Jun Ma; Junhua Yan; Xiyang Zhi; Jinnan Gong

doi:10.3788/AOS202040.2401003

Acta Optica Sinica, Volume. 40, Issue 24, 2401003(2020)

Multiple-Scattering Approximation Model Among Horizontally Adjacent Fields for Three-Dimensional Radiative Transfer in Cloud Remote Sensing

Yin Zhang¹, Hao Yan¹, Jun Ma¹, Junhua Yan^1、*, Xiyang Zhi², and Jinnan Gong²

Author Affiliations

¹Key Laboratory of Space Photoelectric Detection and Perception, Ministry of Industry and Information Technology, Nanjing University of Aeronautics and Astronautics, Nanjing, Jiangsu 210016, China

²Research Center for Space Optical Engineering, Harbin Institute of Technology, Harbin, Heilongjiang 150001, China

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Figures & Tables(12)

Fig. 1. Exchange of radiation flux densities among horizontally adjacent fields in 3D space

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Fig. 2. Schematic of radiation flux densities along horizontal direction and radiation intensities along Gaussian direction

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Fig. 3. Mean relative errors of spectral radiance of pixels. (a) E1; (b) E2; (c) E3; (d) E4

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Fig. 4. Spectral radiance image results and model's errors observed under sub-satellite point at noon. (a) SHDOM; (b) proposed model; (c) IPA model; (d) SSEddMS model

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Fig. 5. Average value of USF of middle layer' grid point in 3D cloud field under varying optical thicknesses. (a) I1; (b) I2; (c) I3; (d) I4

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Fig. 6. Average value of USF of middle layer' grid point in 3D cloud field under varying horizontal non-uniform degree. (a) II1; (b) II2; (c) II3; (d) II4

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Table 1. Parameters of 3D cloud scene

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Table 1. Parameters of 3D cloud scene

Parameter	Cu	Sc	Ac
Average liquid water content /(g·m^-3)	0.93	0.68	0.74
Average extinction coefficient /km^-1	125.9	62.39	81.99
Standard deviation of horizontal extinction coefficient /km^-1	14.2	2.6	5.5
Average single scattering albedo	0.999997	0.999996	0.999996
Altitude range /km	1.66-1.82	0.46-0.62	4.50-4.62
Grid resolution /m	66.7×66.7×40	80×80×40	80×80×40
Grid size	5×5×5
Scattering phase function model	Mie model
Ground temperature /K	288
Ground albedo	0.2
Wavelength /μm	0.67
Note: standard deviation of horizontal extinction coefficient is the standard deviation of extinction coefficient for horizontal surface of cloud scene, indicating horizontal non-uniform degree of the cloud.

Table 2. Mean relative errors of USF obtained by different models

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Table 2. Mean relative errors of USF obtained by different models

Cloud scene	Solar zenithangle /(°)	Mean relative error of USF /%
Cloud scene	Solar zenithangle /(°)	IPA	SSEddMS	Proposed model	Improvement
	0	40.50	25.96	6.93	19.03
	15	42.12	26.76	8.28	18.48
Cu	30	40.49	24.03	10.87	13.16
	45	32.99	16.24	12.06	4.18
	60	19.06	5.71	4.59	1.12
	0	29.85	17.88	2.48	15.40
	15	30.87	18.09	2.88	15.21
Sc	30	27.36	13.27	3.75	9.52
	45	21.98	6.62	6.04	0.58
	60	22.26	8.28	7.83	0.45
	0	32.66	19.87	4.69	15.18
	15	34.02	20.44	4.74	15.70
Ac	30	31.41	16.60	4.83	11.76
	45	25.22	9.61	6.20	3.41
	60	20.65	7.34	5.86	1.48

Table 3. Observing parameters of camera
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Table 3. Observing parameters of camera
Experiment No. θ /(°) φ /(°) X₀ /km Y₀ /km Z₀ /km
E1 0 180 0.135 0.135 401.820
E2 20 180 -136.673 0.135 377.697
E3 40 180 -256.980 0.135 308.238
E4 60 180 -346.275 0.135 201.820

Table 4. Design of cloud scene
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Table 4. Design of cloud scene
Experimentalgroup Scene number Average extinctioncoefficient /km^-1 Standard deviation of horizontalextinction coefficient/km^-1
1 45.9
2 85.9
Experiment I 3 105.9 14.5
4 145.9
1 1.0
Experiment II 2 125.9 10.0
3 20.0
4 30.0

Table 5. Mean relative errors of USF in experiment I and II

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Table 5. Mean relative errors of USF in experiment I and II

Experimentalgroup	Scenenumber	Mean relative error of USF /%
Experimentalgroup	Scenenumber	IPA	SSEddMS	Proposed model	Improvement
	1	30.44	18.13	8.87	9.26
Experiment I	2	31.97	19.41	4.74	14.67
	3	36.71	23.05	5.93	17.12
	4	46.13	30.71	8.61	22.10
	1	41.15	26.49	6.76	19.73
Experiment II	2	40.77	26.20	6.84	19.36
	3	40.10	25.66	7.01	18.65
	4	40.44	26.11	7.58	18.53

Table 6. Computing time of different models
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Table 6. Computing time of different models
N_x N_y N_z Computing time /s Improved ratiowith SHDOM
IPA SSEddMS SHDOM/Numberof iterations Proposedmodel
100 100 20 3.1 4.7 73/49 4.8 15
300 300 20 27.3 46.7 799/48 47.3 17
500 500 20 76 131 2320.2/49 132.1 18

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Yin Zhang, Hao Yan, Jun Ma, Junhua Yan, Xiyang Zhi, Jinnan Gong. Multiple-Scattering Approximation Model Among Horizontally Adjacent Fields for Three-Dimensional Radiative Transfer in Cloud Remote Sensing[J]. Acta Optica Sinica, 2020, 40(24): 2401003

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