Theoretical Dependence of the Near-Asymptotic Apparent Optical Properties on the Inherent Optical Properties of Sea Water*

George F. Beardsley; J. Ronald V. Zaneveld

doi:10.1364/JOSA.59.000373

Journal of the Optical Society of America
Vol. 59,
Issue 4,
pp. 373-377
(1969)
•https://doi.org/10.1364/JOSA.59.000373

Theoretical Dependence of the Near-Asymptotic Apparent Optical Properties on the Inherent Optical Properties of Sea Water

George F. Beardsley and J. Ronald V. Zaneveld

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George F. Beardsley and J. Ronald V. Zaneveld, "Theoretical Dependence of the Near-Asymptotic Apparent Optical Properties on the Inherent Optical Properties of Sea Water*," J. Opt. Soc. Am. 59, 373-377 (1969)

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Abstract

The apparent optical properties of sea water are a set of measurables that describe the geometry of the submarine light field. These properties are related to the inherent optical properties—the volume attenuation coefficient and the volume scattering function—through the process of radiative transfer. A numerical approximation to the equation of radiative transfer was programmed for solution on a high-speed digital computer. The technique is based on resolving the hydrosol into a system of thin slabs, finding approximate transmission and reflection operators for each slab, and then systematically applying these operators to determine the geometry of the light field in the interior of the system of slabs. Thus each set of calculations produces the radiance solid as a function of depth. The apparent optical properties were found by numerical integration of the radiance. A simple three-parameter model was used to simplify study of the dependence of the apparent optical properties on the directional characteristics of the volume scattering function.

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Location	Date	Depth	b/c	Observer
41° N, 70° 55′ W	5/5/66	0 m	0.293	Beardsley
39° 55′ N, 70° 38′ W	4/27/66	0 m	0.258	Beardsley
34° 56.5′ N, 66° 29.5′ W	4/30/66	0 m	0.202	Beardsley
Pend Oreille Lake, Idaho	3/16/57	~30 m	0.697	Tyler, 1960
	4/28/57	~30m	0.715	Tyler, 1960

b/c	0.8	0.8	0.8	0.8	0.2	0.2	0.2	0.2	0.05	0.05	0.05	0.05
ef	0.95	0.95	0.65	0.65	0.95	0.95	0.65	0.65	0.95	0.95	0.65	0.65
eb	0.70	0.30	0.70	0.30	0.70	0.30	0.70	0.30	0.70	0.30	0.70	0.30
F	0.9944	0.99953	0.395	0.881	0.9944	0.99953	0.395	0.881	0.9944	0.99953	0.395	0.881
B	0.0056	0.00047	0.605	0.112	0.0056	0.00047	0.605	0.119	0.0056	0.00047	0.605	0.112
R,%	0.56	0.10	26.6	6.8	0.06	0.005	5.9	1.03	0.013	0.001	1.43	0.223
D(−)	1.31	1.31	1.30	1.39	1.16	1.15	1.16	1.20	1.12	1.12	1.12	1.13
D(+)	2.52	6.67	1.70	2.61	1.91	4.90	1.58	2.65	1.75	3.83	1.54	2.61
K(−)/c	0.316	0.308	0.974	0.671	0.924	0.92	1.13	1.04	1.11	1.11	1.16	1.14
K(+)/c	0.372	0.383	0.976	0.678	0.934	1.00	1.13	1.06	1.11	1.17	1.16	1.16
k/c	0.327	0.319	0.980	0.674	0.938	0.935	1.14	1.06	1.12	1.12	1.17	1.15
$\frac{a_{calc}}{c}$	0.241	0.228	0.405	0.398	0.797	0.800	0.848	0.880	0.991	0.991	1.00	0.984
$\frac{a_{calc}}{a_{true}}$	1.20	1.14	2.02	1.99	0.996	1.00	1.06	1.10	1.04	1.04	1.05	1.03

	Computed	Measured
K(+), m⁻¹	0.275	0.180
K(−), m⁻¹	0.275	⋯
k, m⁻¹	0.275	⋯
D(+)	1.26	1.34
D(−)	3.17	2.79
R,%	0.80	2.80

Location	Date	Depth	b/c	Observer
41° N, 70° 55′ W	5/5/66	0 m	0.293	Beardsley
39° 55′ N, 70° 38′ W	4/27/66	0 m	0.258	Beardsley
34° 56.5′ N, 66° 29.5′ W	4/30/66	0 m	0.202	Beardsley
Pend Oreille Lake, Idaho	3/16/57	~30 m	0.697	Tyler, 1960
	4/28/57	~30m	0.715	Tyler, 1960

b/c	0.8	0.8	0.8	0.8	0.2	0.2	0.2	0.2	0.05	0.05	0.05	0.05
ef	0.95	0.95	0.65	0.65	0.95	0.95	0.65	0.65	0.95	0.95	0.65	0.65
eb	0.70	0.30	0.70	0.30	0.70	0.30	0.70	0.30	0.70	0.30	0.70	0.30
F	0.9944	0.99953	0.395	0.881	0.9944	0.99953	0.395	0.881	0.9944	0.99953	0.395	0.881
B	0.0056	0.00047	0.605	0.112	0.0056	0.00047	0.605	0.119	0.0056	0.00047	0.605	0.112
R,%	0.56	0.10	26.6	6.8	0.06	0.005	5.9	1.03	0.013	0.001	1.43	0.223
D(−)	1.31	1.31	1.30	1.39	1.16	1.15	1.16	1.20	1.12	1.12	1.12	1.13
D(+)	2.52	6.67	1.70	2.61	1.91	4.90	1.58	2.65	1.75	3.83	1.54	2.61
K(−)/c	0.316	0.308	0.974	0.671	0.924	0.92	1.13	1.04	1.11	1.11	1.16	1.14
K(+)/c	0.372	0.383	0.976	0.678	0.934	1.00	1.13	1.06	1.11	1.17	1.16	1.16
k/c	0.327	0.319	0.980	0.674	0.938	0.935	1.14	1.06	1.12	1.12	1.17	1.15
$\frac{a_{calc}}{c}$	0.241	0.228	0.405	0.398	0.797	0.800	0.848	0.880	0.991	0.991	1.00	0.984
$\frac{a_{calc}}{a_{true}}$	1.20	1.14	2.02	1.99	0.996	1.00	1.06	1.10	1.04	1.04	1.05	1.03

Abstract

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Figures (6)

Tables (3)

Equations (13)

Journal of the Optical Society of America