Mie Theory Simulation and Empirical Analysis of Mass-Specific Backscattering Properties of Suspended Particles in the Yellow and East China Seas

Fig. 2. $b_{b p}^{*}$ spectra for all of the data measured during the cruise, and the average spectrum shown with one standard deviation range ( $\bar{x}$ ±s)

Download full size

Fig. 3. Variations of backscattering efficiency $Q_{b b}$ of spherical homogeneous particles with particle diameter D for various wavelengths

Download full size

$Variations of backscattering efficiency Qbb with particle diameter D for various real part of relative refractive index n and imaginary part of relative refractive index n′. (a) Real part of relative refractive index n; (b) imaginary part of relative refractive index n′$

Fig. 4. Variations of backscattering efficiency $Q_{b b}$ with particle diameter D for various real part of relative refractive index n and imaginary part of relative refractive index n′. (a) Real part of relative refractive index n; (b) imaginary part of relative refractive index n′

Download full size

Fig. 5. Theoretical relationship between $b_{b p}^{*} (532)$ and ξ. In this figure, the light dashed lines represent the algae particles, the light solid lines represent the inorganic mineral particles, and the two black dotted lines represent the fitting curves of algae particles and inorganic mineral particles under the average condition

Download full size

$Theoretical relationship between bbp*(532) and the real part of the relative refractive index n of particles for various apparent density ρa when ξ is 4.0. The scattered points marked in the figure represent the bbp*(532) theoretical values of different algae and inorganic mineral particles at their corresponding n and ρa$

Fig. 6. Theoretical relationship between $b_{b p}^{*} (532)$ and the real part of the relative refractive index n of particles for various apparent density ρ_a when ξ is 4.0. The scattered points marked in the figure represent the $b_{b p}^{*} (532)$ theoretical values of different algae and inorganic mineral particles at their corresponding n and ρ_a

Download full size

Fig. 7. $b_{b p}^{*}$ spectra of Dunaliella bioculata simulated under different n′ value

Download full size

Fig. 8. Relationship between $b_{b p}^{*}$ spectral slope η and characteristic parameters of particles. (a) η versus suspended particle concentration C_SPM; (b) η versus the proportion of organic particles mass concentration C_POM/C_SPM

Download full size

Fig. 9. Relationship between $b_{b p} (532)$ and C_SPM in the logarithmic coordinate system

Download full size

Fig. 10. Relational model between the measured $b_{b p}^{*} (532)$ and C_POM/C_SPM. The dashed line and thin solid line in the figure represent the simulation results with different values of particle size distribution slopes ξ, the circular scatter points represent in situ sampling points, and the bold solid line represents the power-law fitting results for in situ data

Download full size

Fig. 11. Relational model between the measured $b_{b p}^{*} (532)$ and C_POM/C_SPMfor the group A and group B. (a) Group A; (b) group B

Download full size

Table 1. Statistical results of in situ measured data

View table

Table 1. Statistical results of in situ measured data

Parameter	Minimum	Maximum	Average	Median	SD	CV /%
$b_{b p} (442)$ /（10^-2 m^-1）	0.38	111.24	8.49	0.96	19.00	223.0
$b_{b p} (488)$ /（10^-2 m^-1）	0.27	89.14	7.20	0.84	16.00	216.0
$b_{b p} (532)$ /（10^-2 m^-1）	0.19	88.66	7.02	0.70	15.00	220.0
$b_{b p} (589)$ /（10^-2 m^-1）	0.15	87.70	6.76	0.60	15.00	225.0
$b_{b p} (676)$ /（10^-2 m^-1）	0.11	75.57	5.84	0.51	13.00	225.0
$b_{b p} (852)$ /（10^-2 m^-1）	0.07	63.38	4.85	0.42	11.00	226.0
C_SPM /（g·m^-3）	0.40	95.30	8.91	1.90	18.00	197.0
C_PIM /（g·m^-3）	0.10	88.60	7.66	1.00	17.00	216.0
C_POM /（g·m^-3）	0.20	6.70	1.26	1.00	1.08	86.3
C_POM/C_SPM/10^-1	0.48	8.42	4.44	4.55	2.46	55.5
$b_{b p}^{*}$ spectral slop η	0.53	2.46	1.29	1.22	0.48	37.4
$b_{b p}^{*} (532)$ /（10^-3 m²·g^-1）	2.22	17.50	5.43	4.58	2.89	53.3
$b_{b p}^{*} (676)$ /（10^-3 m²·g^-1）	1.53	14.11	4.12	3.21	2.55	61.8

Table 2. Setting of main parameters of Mie calculations

View table

Table 2. Setting of main parameters of Mie calculations

Parameter	Value（Increments are given in parentheses）	Reference
λ /nm	442，488，532，589，676，852	—
D /μm	0.02（Set 200 points at logarithmic intervals）200	Babin et al.^［16］；Zhou et al.^［22］
n	1.01（0.02）1.27	Mobley^［19］；Bricaud et al.^［23］
n′	0，0.001，0.005	Bricaud et al.^［18］；Ahn et al.^［24］
ξ	3.0（0.2）5.0	Babin et al.^［16］
ρ_a /（10⁶ g·m^-3）	0.3（0.3）5.1	Woźniak et al.^［17］；Aas^［25］

Table 3. $b_{b p}^{*} (532)$ values of different algal particles, assuming n′=0 and ξ value as indicated

View table

Table 3. $b_{b p}^{*} (532)$ values of different algal particles, assuming n′=0 and ξ value as indicated

Algae particle type	n	ρ_a/（10⁶ g·m^-3）	$b_{b p}^{*} (532)$ /（10^-3 m²·g^-1）
Algae particle type	n	ρ_a/（10⁶ g·m^-3）	ξ=3.8	ξ=4.0	ξ=4.2
Average	1.0587	0.535	1.95	4.09	8.39
Green algae	1.0558	0.492	1.88	3.96	8.14
Diatoms	1.0566	0.614	1.55	3.27	6.72
Blue-green algae	1.0574	0.501	1.96	4.13	8.48
Dinoflagellates	1.0604	0.496	2.22	4.66	9.53
Coccolithophorids	1.0631	0.570	2.12	4.44	9.08

Table 4. $b_{b p}^{*} (532)$ of the typical mineral particles in coastal waters, assuming n′=0 and ξ value as indicated

View table

Table 4. $b_{b p}^{*} (532)$ of the typical mineral particles in coastal waters, assuming n′=0 and ξ value as indicated

Mineral particle type	n	ρ_a/（10⁶ g·m^-3）	$b_{b p}^{*} (532)$ /（10^-3 m²·g^-1）
Mineral particle type	n	ρ_a/（10⁶ g·m^-3）	ξ=3.8	ξ=4.0	ξ=4.2
Average	1.168	2.61	4.68	9.12	17.35
Opal	1.075	1.90	0.94	1.95	3.93
Quartz	1.156	2.65	3.83	7.41	14.08
Kaolinite	1.164	2.65	4.30	8.30	15.73
Montmorillonite	1.167	2.50	4.72	9.13	17.32
Calcite	1.173	2.71	4.69	9.10	17.24
Gibbsite	1.177	2.42	5.49	10.67	20.25
Illite	1.179	2.80	4.87	9.46	17.94
Chlorite	1.206	3.00	6.09	11.93	22.65
Aragonite	1.218	2.83	7.18	14.16	27.00

Table 5. Type and content ratio of main inorganic minerals in the Yellow and East China Seas

View table

Table 5. Type and content ratio of main inorganic minerals in the Yellow and East China Seas

Mineral particle type	Illite	Chlorite	Kaolinite	Montmorillonite	Reference
Proportion /%	61.00	17.06	13.94	8.00	Wei et al.^［30］
	61.80	9.40	13.00	15.80	Song et al.^［31］
	61.90	10.00	13.10	15.00	Zhang et al.^［32］
Average /%	62.00	12.00	13.00	13.00	This study

Table 6. $b_{b p}^{} (532)$ value at different imaginary parts of relative refractive index n′ and its changing rate compared with the case without absorption, taking Diatoms* as example

View table

Table 6. $b_{b p}^{} (532)$ value at different imaginary parts of relative refractive index n′ and its changing rate compared with the case without absorption, taking Diatoms* as example

ξ	$b_{b p}^{*} (532)$ /（10^-3 m²·g^-1）（Changing rate/%）
ξ	n′=0.001	n′=0.005
3.6	0.64（-15.76）	0.55（-28.11）
3.8	1.43（-7.79）	1.31（-15.38）
4.0	3.15（-3.63）	3.01（-7.99）
4.2	6.60（-1.72）	6.44（-4.18）
4.4	13.03（-0.88）	12.84（-2.27）

Table 7. Correlation analysis of in situ measured data (P <0.05)

View table

Table 7. Correlation analysis of in situ measured data (P <0.05)

Parameter	C_SPM	C_PIM	C_POM	C_POM/C_SPM	$b_{b p} (532)$	$b_{b p}^{*} (532)$	η
C_SPM	1.00
C_PIM	1.00	1.00
C_POM	0.93	0.92	1.00
C_POM/C_SPM	-0.62	-0.62	-0.58	1.00
$b_{b p} (532)$	0.96	0.96	0.87	-0.61	1.00
$b_{b p}^{*} (532)$	0.43	0.43	0.37	-0.62	0.58	1.00
η	-0.51	-0.50	-0.61	0.75	-0.48	-0.54	1.00

Table 8. Coefficients of the linear fitting relationship ( $b_{b p}^{*} (532) = c_{1} C_{P O M} / C_{S P M} + c_{2}$ ) between $C_{P O M} / C_{S P M}$ ratio and $b_{b p}^{*} (532)$ of the mixed particles simulated by assuming different ξ
View table
Table 8. Coefficients of the linear fitting relationship ( $b_{b p}^{*} (532) = c_{1} C_{P O M} / C_{S P M} + c_{2}$ ) between $C_{P O M} / C_{S P M}$ ratio and $b_{b p}^{*} (532)$ of the mixed particles simulated by assuming different ξ
ξ c₁ c₂
3.6 -0.0017 0.0025
3.8 -0.0033 0.0049
4.0 -0.0062 0.0096
4.2 -0.0113 0.0182
4.4 -0.0198 0.0333

Tools

Get Citation

Copy Citation Text

Shuang Cao, Bing Han, Jianhua Zhu, Zhifeng Li. Mie Theory Simulation and Empirical Analysis of Mass-Specific Backscattering Properties of Suspended Particles in the Yellow and East China Seas[J]. Laser & Optoelectronics Progress, 2022, 59(13): 1301002

Download Citation

EndNote(RIS)BibTex Plain Text

Set citation alerts for article

Save article for my favorites

Paper Information

Category: Atmospheric Optics and Oceanic Optics

Received: Feb. 6, 2022

Accepted: Feb. 28, 2022

Published Online: Jun. 9, 2022

The Author Email: Bing Han (hotrice@sina.com)

DOI:10.3788/LOP202259.1301002

Topics

laser devices and laser physics

Lasers and Laser Optics

Laser physics

laser manufacturing

Instrumentation, Measurement and Metrology

Table 1. Statistical results of in situ measured data

Table 1. Statistical results of in situ measured data

Table 2. Setting of main parameters of Mie calculations

Table 2. Setting of main parameters of Mie calculations

Table 3. $b_{b p}^{*} (532)$ values of different algal particles, assuming n′=0 and ξ value as indicated

Table 3. $b_{b p}^{*} (532)$ values of different algal particles, assuming n′=0 and ξ value as indicated

Table 4. $b_{b p}^{*} (532)$ of the typical mineral particles in coastal waters, assuming n′=0 and ξ value as indicated

Table 4. $b_{b p}^{*} (532)$ of the typical mineral particles in coastal waters, assuming n′=0 and ξ value as indicated

Table 5. Type and content ratio of main inorganic minerals in the Yellow and East China Seas

Table 5. Type and content ratio of main inorganic minerals in the Yellow and East China Seas

Table 6. $b_{b p}^{} (532)$ value at different imaginary parts of relative refractive index n′ and its changing rate compared with the case without absorption, taking Diatoms* as example

Table 6. $b_{b p}^{} (532)$ value at different imaginary parts of relative refractive index n′ and its changing rate compared with the case without absorption, taking Diatoms* as example

Table 7. Correlation analysis of in situ measured data (P <0.05)

Table 7. Correlation analysis of in situ measured data (P <0.05)

Table 8. Coefficients of the linear fitting relationship ( $b_{b p}^{} (532) = c_{1} C_{P O M} / C_{S P M} + c_{2}$ ) between $C_{P O M} / C_{S P M}$ ratio and $b_{b p}^{} (532)$ of the mixed particles simulated by assuming different ξ

Table 8. Coefficients of the linear fitting relationship ( $b_{b p}^{} (532) = c_{1} C_{P O M} / C_{S P M} + c_{2}$ ) between $C_{P O M} / C_{S P M}$ ratio and $b_{b p}^{} (532)$ of the mixed particles simulated by assuming different ξ

Table 1. Statistical results of in situ measured data

Table 1. Statistical results of in situ measured data

Table 2. Setting of main parameters of Mie calculations

Table 2. Setting of main parameters of Mie calculations

Table 3. bbp*(532) values of different algal particles, assuming n′=0 and ξ value as indicated

Table 3. bbp*(532) values of different algal particles, assuming n′=0 and ξ value as indicated

Table 4. bbp* (532) of the typical mineral particles in coastal waters, assuming n′=0 and ξ value as indicated

Table 4. bbp* (532) of the typical mineral particles in coastal waters, assuming n′=0 and ξ value as indicated

Table 5. Type and content ratio of main inorganic minerals in the Yellow and East China Seas

Table 5. Type and content ratio of main inorganic minerals in the Yellow and East China Seas

Table 6. bbp*(532) value at different imaginary parts of relative refractive index n′ and its changing rate compared with the case without absorption, taking Diatoms as example

Table 6. bbp*(532) value at different imaginary parts of relative refractive index n′ and its changing rate compared with the case without absorption, taking Diatoms as example

Table 7. Correlation analysis of in situ measured data (P <0.05)

Table 7. Correlation analysis of in situ measured data (P <0.05)

Table 8. Coefficients of the linear fitting relationship (bbp*(532)=c1 CPOM/CSPM+c2) between CPOM/CSPMratio and bbp*(532) of the mixed particles simulated by assuming different ξ

Table 8. Coefficients of the linear fitting relationship (bbp*(532)=c1 CPOM/CSPM+c2) between CPOM/CSPMratio and bbp*(532) of the mixed particles simulated by assuming different ξ

Table 3. $b_{b p}^{*} (532)$ values of different algal particles, assuming n′=0 and ξ value as indicated

Table 3. $b_{b p}^{*} (532)$ values of different algal particles, assuming n′=0 and ξ value as indicated

Table 4. $b_{b p}^{*} (532)$ of the typical mineral particles in coastal waters, assuming n′=0 and ξ value as indicated

Table 4. $b_{b p}^{*} (532)$ of the typical mineral particles in coastal waters, assuming n′=0 and ξ value as indicated

Table 6. $b_{b p}^{} (532)$ value at different imaginary parts of relative refractive index n′ and its changing rate compared with the case without absorption, taking Diatoms* as example

Table 6. $b_{b p}^{} (532)$ value at different imaginary parts of relative refractive index n′ and its changing rate compared with the case without absorption, taking Diatoms* as example

Table 8. Coefficients of the linear fitting relationship ( $b_{b p}^{} (532) = c_{1} C_{P O M} / C_{S P M} + c_{2}$ ) between $C_{P O M} / C_{S P M}$ ratio and $b_{b p}^{} (532)$ of the mixed particles simulated by assuming different ξ

Table 8. Coefficients of the linear fitting relationship ( $b_{b p}^{} (532) = c_{1} C_{P O M} / C_{S P M} + c_{2}$ ) between $C_{P O M} / C_{S P M}$ ratio and $b_{b p}^{} (532)$ of the mixed particles simulated by assuming different ξ