Maximum Correlated <i>k</i>-Distribution Optimal Algorithm for Single-Scattering Parameters in Cloudy Atmospheres

Yin Zhang; Shaoshuai Zhang; Hao Yan; Yiwei Fan; Guiyi Zhu; Junhua Yan

doi:10.3788/AOS222030

Acta Optica Sinica, Volume. 43, Issue 18, 1801001(2023)

Maximum Correlated k-Distribution Optimal Algorithm for Single-Scattering Parameters in Cloudy Atmospheres

Yin Zhang, Shaoshuai Zhang, Hao Yan, Yiwei Fan, Guiyi Zhu, and Junhua Yan^*

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

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Figures & Tables(17)

Fig. 1. Spectral parameter distribution curves of a cloudy atmosphere under different temperatures, atmospheric pressures, particle effective radii, and water contents. (a) Cloudy atmosphere extinction coefficient; (b) cloudy atmosphere single-scattering albedo; (c) cloudy atmosphere asymmetry factor

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Fig. 2. Spectral distribution curves of single-scattering albedo. (a) Cloud single-scattering albedo; (b) cloudy atmosphere single-scattering albedo

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Fig. 3. Schematic of the maximal correlated parameter grouping method

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Fig. 4. Schematic of solving number of quadrature intervals in each group

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Fig. 5. Schematic of the rearrangement of spectral parameters and the solution of average equivalent parameters

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Fig. 6. Schematic of average extinction coefficient and processed average extinction coefficient in cloudy areas. (a) Spectral distribution of cloudy average extinction coefficient; (b) cloudy average extinction coefficient in g space;(c) cloudy average extinction coefficient after scaling; (d) average extinction coefficient after scaling in g space

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Fig. 7. MRE changing with the increasing interval amount when calculating upwelling radiance for the cloudy atmosphere using different CKD methods. (a) Band b1; (b) band b2; (c) band b3; (d) band b4

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Fig. 8. Scheme of the maximal correlated parameter grouping situation in band b3 when number of the quadrature intervals is greater than two

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Fig. 9. In band b3, spectrum distribution curves of parameters in a cloudy atmosphere, rearrangement of these parameters and average equivalent parameters in each interval when number of quadrature intervals is eight. (a)(b) Extinction coefficient; (c)(d) asymmetry factor; (e)(f) single-scattering albedo; (g)(h) solar flux density

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Table 1. Visible and near-infrared surface radiation accounted for the proportion of total upward radiation

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Table 1. Visible and near-infrared surface radiation accounted for the proportion of total upward radiation

Cloud type	Base /km	Top /km	Cloud extinction coefficient /km^-1	Optical thickness	Proportion
As	2.400	3.000	128.1	76.9	5.4×10^-35
Ns	0.160	0.660	92.6	46.3	2.6×10^-21
Sc	0.660	1.000	38.7	13.2	9.5×10^-7
Sc	0.660	0.860	38.7	7.74	2.7×10^-4
Sc	0.660	0.760	38.7	3.87	1.6×10^-2
Sc	0.660	0.715	38.7	2.12	1.0×10^-1

Table 2. Parameters of the cloudy atmosphere scene

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Table 2. Parameters of the cloudy atmosphere scene

Parameter	Content
Atmospheric model	1976 U.S. standard atmosphere
Atmospheric altitude range/km	0-100
Absorber	H₂O，CO₂，CH₄，N₂O，O₃，CO，N₂，O₂
Scattering phase function model	H-G model
Ground temperature /K	288
Ground albedo	0.03
Cloud type	Cu
Altitude range of cloud /km	4.02-5.22
Vertical resolution /km	0.04
Average liquid water content of cloud /（g∙m^-3）	0.16
Average particle effective radius of cloud /μm	6.10

Table 3. Band setting and the corresponding average atmospheric transmittance
View table
Table 3. Band setting and the corresponding average atmospheric transmittance
Band No. Band range /μm Wavenumber range /cm^-1 Average transmittance
b1 2.20-2.40 4165-4545 0.8847
b2 1.80-1.95 5125-5555 0.0293
b3 1.50-2.00 5000-6665 0.6537
b4 2.30-2.60 384-4350 0.4281

Table 4. Group and intra-group quadrature weights in band b3 at number of quadrature intervals equaling to eight
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Table 4. Group and intra-group quadrature weights in band b3 at number of quadrature intervals equaling to eight
Group Maximal correlated parameter Integral weight between groups Quadrature weight
1 $F_{T O A}$ 0.4887 0.4380 0.0756 0.0885 0.3980
2 $ω$ 0.5113 0.0505 0.1756 0.1609 0.6130

Table 5. Experimental design of clouds at different heights
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Table 5. Experimental design of clouds at different heights
Scene No. Band number Altitude range of cloud /km
1 b3 1.02-2.22
2 4.02-5.22
3 9.02-10.22

Table 6. MRE calculated by different methods in cloud scenes at different altitudes
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Table 6. MRE calculated by different methods in cloud scenes at different altitudes
Scene No. MRE of radiance /%
$Δ l o g k$ PCOP-CKD SSP-MCKD
Average error 28.60 7.31 1.68
1 32.69 5.30 0.47
2 27.07 7.53 4.30
3 26.05 9.10 0.26

Table 7. Experimental design of cloud scenes with different particle effective radii and water content

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Table 7. Experimental design of cloud scenes with different particle effective radii and water content

Cloud scene	Scene No.	Average particle effective radius of cloud /μm	Average liquid water content of cloud / （g∙m^-3）	Average cloud extinction coefficient /km^-1	Standard deviation of cloud extinction coefficient /km^-1
Cu	S1	6.10	0.16	45.38	21.75
Sc	S2	12.42	0.23	30.27	14.32
	S3	14.72	0.52	57.20	37.42
	S4	16.05	0.68	67.18	5.60
Ac	S5	13.72	0.36	42.64	11.53
	S6	15.52	0.50	52.02	13.32
	S7	16.02	0.58	58.37	17.46

Table 8. MRE calculated by different methods in cloud scenes with different optical properties
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Table 8. MRE calculated by different methods in cloud scenes with different optical properties
Scene No. MRE of radiance /%
$Δ l o g k$ PCOP-CKD SSP-MCKD
Average error 23.27 8.85 5.54
S1 27.07 7.53 4.30
S2 14.68 3.32 2.03
S3 31.23 18.32 13.67
S4 21.98 5.79 3.51
S5 16.32 6.86 1.54
S6 23.89 8.17 6.32
S7 27.75 11.96 7.44

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Yin Zhang, Shaoshuai Zhang, Hao Yan, Yiwei Fan, Guiyi Zhu, Junhua Yan. Maximum Correlated k-Distribution Optimal Algorithm for Single-Scattering Parameters in Cloudy Atmospheres[J]. Acta Optica Sinica, 2023, 43(18): 1801001

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Paper Information

Category: Atmospheric Optics and Oceanic Optics

Received: Nov. 22, 2022

Accepted: Feb. 7, 2023

Published Online: Sep. 4, 2023

The Author Email: Yan Junhua (yjh9758@126.com)

DOI:10.3788/AOS222030

Topics

laser devices and laser physics

Lasers and Laser Optics

Laser physics

laser manufacturing

Instrumentation, Measurement and Metrology

Table 1. Visible and near-infrared surface radiation accounted for the proportion of total upward radiation

Table 1. Visible and near-infrared surface radiation accounted for the proportion of total upward radiation

Table 2. Parameters of the cloudy atmosphere scene

Table 2. Parameters of the cloudy atmosphere scene

Table 3. Band setting and the corresponding average atmospheric transmittance

Table 3. Band setting and the corresponding average atmospheric transmittance

Table 4. Group and intra-group quadrature weights in band b3 at number of quadrature intervals equaling to eight

Table 4. Group and intra-group quadrature weights in band b3 at number of quadrature intervals equaling to eight

Table 5. Experimental design of clouds at different heights

Table 5. Experimental design of clouds at different heights

Table 6. MRE calculated by different methods in cloud scenes at different altitudes

Table 6. MRE calculated by different methods in cloud scenes at different altitudes

Table 7. Experimental design of cloud scenes with different particle effective radii and water content

Table 7. Experimental design of cloud scenes with different particle effective radii and water content

Table 8. MRE calculated by different methods in cloud scenes with different optical properties

Table 8. MRE calculated by different methods in cloud scenes with different optical properties