Irradiance Reflectivity of a Flat Ocean as a Function of Its Optical
Properties

Howard R. Gordon; Otis B. Brown

doi:10.1364/AO.12.001549

Applied Optics
Vol. 12,
Issue 7,
pp. 1549-1551
(1973)
•https://doi.org/10.1364/AO.12.001549

Irradiance Reflectivity of a Flat Ocean as a Function of Its Optical Properties

Howard R. Gordon and Otis B. Brown

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Howard R. Gordon and Otis B. Brown, "Irradiance Reflectivity of a Flat Ocean as a Function of Its Optical Properties," Appl. Opt. 12, 1549-1551 (1973)

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Abstract

The radiative transfer equation has been solved by a Monte Carlo technique for a flat homogeneous ocean with two different incident radiance distributions. The irradiance reflectivity R for photons that penetrate the ocean is presented as a function of the single scattering albedo ω₀, and the scattering phase function P(θ) of the medium. The P(θ)’s used are based on experimental observations. The results clearly show that R depends strongly on both ω₀ and P(θ) but apparently not on the form of the incident radiance distribution. Arguments are presented to show that in clearest ocean water the upwelling field above the surface can provide information only about the upper 25 m of the medium.

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θ (deg)	A (×10³)	B (×10³)	C (×10³)
0	10924	10171	9521
1	4916	4577	4285
5	573.5	534.0	499.9
10	169.3	157.7	147.6
20	29.5	29.39	29.21
30	12.56	11.95	11.42
45	3.059	3.661	4.189
60	1.092	1.577	1.999
75	0.546	0.915	1.190
90	0.344	0.661	0.952
105	0.311	0.641	0.928
120	0.317	0.732	1.094
135	0.410	0.829	1.309
150	0.492	1.017	1.618
165	0.579	1.261	1.856
180	0.617	,1.357	1.999

	A		B		C

ω₀	Sun	Sky	Sun	Sky	Sun	Sky
0	0	0	0	0	0	0
0.2	0.0012	0.0011	0.0024	0.0023	0.0036	0.0034
0.4	0.0030	0.0029	0.0063	0.0062	0.0093	0.0091
0.5	0.0044	0.0043	0.0094	0.0089	0.0136	0.0131
0.6	0.0068	0.0066	0.0138	0.0133	0.0199	0.0192
0.7	0.0101	0.0099	0.0212	0.0203	0.0303	0.6293
0.75	0.0133	0.0129	0.0268	0.0260	0.0373	0.0367
0.8	0.0176	0.0176	0.0348	0.0339	0.0477	0.0474
0.85	0.0252	0.0255	0.0478	0.0472	0.0651	0.0638
0.9	0.0408	0.0409	0.0708	0.0711	0.0943	0.0940
0.95	0.0816	0.0841	0.1306	0.1303	0.1623	0.1631
Est. Ave. Error (%)	1.64	1.65	1.19	1.22	0.95	0.97

	A		B		C

ω₀	Sun	Sky	Sun	Sky	Sun	Sky
0	0	0	0	0	0	0
0.2	1.16	1.03	1.10	1.03	1.12	1.01
0.4	1.52	1.37	1.46	1.34	1.40	1.31
0.5	1.80	1.64	1.74	1.59	1.66	1.55
0.6	2.16	1.98	2.06	1.88	1.97	1.83
0.7	2.75	2.52	2.55	2.40	2.46	2.28
0.75	3.24	2.99	3.00	2.78	2.80	2.62
0.8	3.96	3.66	3.63	3.27	3.32	3.09
0.85	5.00	4.72	4.35	4.06	4.04	3.72
0.9	6.91	6.43	5.83	5.47	5.35	5.00
0.95	11.48	10.30	9.38	8.61	8.23	7.73

θ (deg)	A (×10³)	B (×10³)	C (×10³)
0	10924	10171	9521
1	4916	4577	4285
5	573.5	534.0	499.9
10	169.3	157.7	147.6
20	29.5	29.39	29.21
30	12.56	11.95	11.42
45	3.059	3.661	4.189
60	1.092	1.577	1.999
75	0.546	0.915	1.190
90	0.344	0.661	0.952
105	0.311	0.641	0.928
120	0.317	0.732	1.094
135	0.410	0.829	1.309
150	0.492	1.017	1.618
165	0.579	1.261	1.856
180	0.617	,1.357	1.999

	A		B		C

ω₀	Sun	Sky	Sun	Sky	Sun	Sky
0	0	0	0	0	0	0
0.2	0.0012	0.0011	0.0024	0.0023	0.0036	0.0034
0.4	0.0030	0.0029	0.0063	0.0062	0.0093	0.0091
0.5	0.0044	0.0043	0.0094	0.0089	0.0136	0.0131
0.6	0.0068	0.0066	0.0138	0.0133	0.0199	0.0192
0.7	0.0101	0.0099	0.0212	0.0203	0.0303	0.6293
0.75	0.0133	0.0129	0.0268	0.0260	0.0373	0.0367
0.8	0.0176	0.0176	0.0348	0.0339	0.0477	0.0474
0.85	0.0252	0.0255	0.0478	0.0472	0.0651	0.0638
0.9	0.0408	0.0409	0.0708	0.0711	0.0943	0.0940
0.95	0.0816	0.0841	0.1306	0.1303	0.1623	0.1631
Est. Ave. Error (%)	1.64	1.65	1.19	1.22	0.95	0.97

Abstract

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Tables (3)

Equations (2)

Applied Optics