Significant relationship between the backward scattering coefficient of sea water and the scatterance at 120°

Tomohiko Oishi

doi:10.1364/AO.29.004658

Significant relationship between the backward scattering coefficient of sea water and the scatterance at 120°

Tomohiko Oishi

Applied Optics
Vol. 29,
Issue 31,
pp. 4658-4665
(1990)
•https://doi.org/10.1364/AO.29.004658

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Tomohiko Oishi, "Significant relationship between the backward scattering coefficient of sea water and the scatterance at 120°," Appl. Opt. 29, 4658-4665 (1990)

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- Original Manuscript: September 14, 1989
- Published: November 1, 1990

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Abstract

Computations of Mie scattering by marine particles indicate that the ratios between the backward scattering coefficient and the scatterance at 120° are ~6.9 ± 0.4, 7.2 ± 0.6, and 7.1 ± 0.5 for Junge, normal and log-normal particle size distributions, respectively. In situ observations of the scattering confirm this result.

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ξ	2.4	2.6	2.8	3.0	3.2	3.4	3.6	Average
1.01 - 0.00i	7.28	7.11	6.97	6.89	6.83	6.74	6.75	6.94
1.02 - 0.00i	7.03	7.00	6.89	6.83	6.80	6.77	6.77	6.87
1.03 - 0.00i	6.89	6.89	6.86	6.80	6.77	6.75	6.75	6.82
1.05 - 0.00i	7.37	7.14	7.00	6.89	6.80	6.77	6.75	6.96
1.08 - 0.00i	7.45	7.23	7.03	6.94	6.86	6.80	6.77	7.01
1.10 - 0.00i	8.86	8.27	7.71	7.27	7.06	6.92	6.86	7.56
1.15 - 0.00i	6.80	6.80	6.77	6.77	6.72	6.77	6.80	6.78
1.20 - 0.00i	4.77	5.25	5.73	6.12	6.41	6.58	6.69	5.94
1.01 - 0.01i	7.06	6.94	6.89	6.83	6.77	6.75	6.75	6.86
1.02 - 0.01i	6.97	6.92	6.89	6.83	6.77	6.75	6.75	6.84
1.03 - 0.01i	6.89	6.89	6.86	6.80	6.77	6.77	6.75	6.82
1.05 - 0.01i	6.97	6.92	6.86	6.83	6.77	6.77	6.75	6.84
1.08 - 0.01i	7.03	6.92	6.89	6.86	6.80	6.77	6.75	6.86
1.10 - 0.01i	7.42	7.17	7.08	6.97	6.89	6.83	6.80	7.02
1.15 - 0.01i	6.72	6.77	6.80	6.83	6.83	6.83	6.80	6.80
1.20 - 0.01i	6.24	6.44	6.58	6.69	6.75	6.77	6.80	6.61
Average	6.98	6.92	6.86	6.82	6.79	6.77	6.77	6.84

Phytoplankton Model	Normal Size Distribution	Log-normal Size Distribution
Refractive Index (imaginary part)	1.01 – 1.05 (0.01)	1.01 – 1.05 (0.01)
Refractive Index (imaginary part)	0.0 and 0.01	0.0 and 0.01
Mean Size of Phytoplankton	30.0 – 100.0 (10.0)	0.69 – 2.07(0.23)
Mean Size of Phytoplankton	(linear scale)	(log scale)
Standard Deviation	1.0 – 15.0 (1.0)	0.05 – 0.5 (0.05)
Standard Deviation	(linear scale)	(log scale)
Total number of phytoplankton bloom model	1120	700

Author	Number of function	Scattering Angle (degrees)	Wavelength (nm)	Area
Austin28 (1973)	27	10 – 170	530	off Ecuador
Kullenberg29 (1968)	2	10 – 165	460,655	Sargasso Sea
Kullenberg30 (1969)	9	10 – 165	525,655	Baltic Sea
			440–460
Kullenberg31 (1972)	16	10 – 150	633	Mediterrenean
Joyce et al.32(1976)	2	8 – 160	520	Polar front
(Kullenberg)
Petzold33 (1972)	3	10 – 170	530	Tongue of Ocean
	2	10 – 170	530	off California
	3	10 – 170	530	San Diego Harbor
Tucker34 (1973)	66	10 – 160	534	San Diego Harbor and off San Diego
Tyler35 (1961)	4	20 – (180)	522	Pacific Coast
	2	20 – (180)	490	Lake Pend Oreille
Whitlock et al.36 (1981)	24*	25 – 155	450,500,550	Appomatto and
	(3 samples)		600,650,700	Back Rivers
			750,800

Angle (degrees)	Regression Line	Correlation Coefficient	Determination Coeffieint
90	4.45 ^* β(90) + 5.01 ^* 10⁻⁴ m⁻¹	0.999	0.998
100	5.66 ^* β (100) + 3.34 ^* 10⁻⁴ m⁻¹	0.999	0.998
110	6.63 ^* β (110) + 1.63 ^* 10⁻⁴ m⁻¹	0.999	0.998
120	7.19 ^* β (120) −0.43 ^* 10⁻⁴ m⁻¹	~1.000	0.999
130	7.53 ^* β (130) −2.17 ^* 10⁻⁴ m⁻¹	0.999	0.998
140	6.78 ^* β (140) −1.62 ^* 10⁻⁴ m⁻¹	0.998	0.996
150	6.31 ^* β (150) −2.70 ^* 10⁻⁴ m⁻¹	0.996	0.992
160	5.87 ^* β (160) −4.44 ^* 10⁻⁴ m⁻¹	0.995	0.990
170	5.26 ^* β (170) −6.12 ^* 10⁻⁴ m⁻¹	0.990	0.980
180	4.73 ^* β (180) −7.47 ^* 10⁻⁴ m⁻¹	0.981	0.962

Angle (degrees)	Percent of data points within ± 10% prediction error (%)	Maximum prediction error (%)
90	60.4	81.4
100	68.7	53.0
110	83.6	26.9
120	94.0	23.3
	(91.8)*	(30.1)*
130	85.1	31.8
140	79.1	17.7
150	77.6	31.1
160	43.3	64.2
170	23.1	106.5
180	14.2	213.0

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