Analytic algorithms for determining radiative transfer optical properties of ocean waters

Ayşe Kaşkaş; Mustafa Ç. Güleçyüz; Cevdet Tezcan; Norman J. McCormick

doi:10.1364/AO.45.007698

Applied Optics
Vol. 45,
Issue 29,
pp. 7698-7705
(2006)
•https://doi.org/10.1364/AO.45.007698

Analytic algorithms for determining radiative transfer optical properties of ocean waters

Ayşe Kaşkaş, Mustafa Ç. Güleçyüz, Cevdet Tezcan, and Norman J. McCormick

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Ayşe Kaşkaş, Mustafa Ç. Güleçyüz, Cevdet Tezcan, and Norman J. McCormick, "Analytic algorithms for determining radiative transfer optical properties of ocean waters," Appl. Opt. 45, 7698-7705 (2006)

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Abstract

A synthetic model for the scattering phase function is used to develop simple algebraic equations, valid for any water type, for evaluating the ratio of the backscattering to absorption coefficients of spatially uniform, very deep waters with data from upward and downward planar irradiances and the remotely sensed reflectance. The phase function is a variable combination of a forward-directed Dirac delta function plus isotropic scattering, which is an elementary model for strongly forward scattering such as that encountered in oceanic optics applications. The incident illumination at the surface is taken to be diffuse plus a collimated beam. The algorithms are compared with other analytic correlations that were previously derived from extensive numerical simulations, and they are also numerically tested with forward problem results computed with a modified F _N method.

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Equations (59)

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ω	g	Correct ϖ	Eq. (20)	Eq. (21)	Approximation (28)	Approximation (29)
0.3	0	0.3	0.29998	0.30000	0.25796	0.31672
0.5	0	0.5	0.49998	0.50000	0.44591	0.51761
0.7	0	0.7	0.69999	0.70000	0.64995	0.71228
0.9	0	0.9	0.90000	0.90000	0.87528	0.90345
0.3	0.7	0.11392	0.11391	0.11392	0.09493	0.12270
0.5	0.7	0.23077	0.23075	0.23077	0.19608	0.24540
0.7	0.7	0.41176	0.41175	0.41176	0.36121	0.42986
0.9	0.7	0.72973	0.72972	0.72973	0.68192	0.74083
0.3	0.9	0.04110	0.04109	0.04110	0.03385	0.04463
0.5	0.9	0.09091	0.09090	0.09091	0.07547	0.09816
0.7	0.9	0.18919	0.18917	0.18919	0.15963	0.20208
0.9	0.9	0.47368	0.47367	0.47368	0.42034	0.49158

ω	g	Correct ϖ	Eq. (20)	Eq. (21)	Approximation (28)	Approximation (29)
0.3	0	0.3	0.29999	0.29999	0.30671	0.29999
0.5	0	0.5	0.49998	0.49999	0.51703	0.49999
0.7	0	0.7	0.69997	0.69999	0.72729	0.69999
0.9	0	0.9	0.89995	0.90000	0.91995	0.90000
0.3	0.7	0.11392	0.11392	0.11392	0.11494	0.11392
0.5	0.7	0.23077	0.23077	0.23077	0.23482	0.23077
0.7	0.7	0.41176	0.41174	0.41175	0.42388	0.41175
0.9	0.7	0.72972	0.72970	0.72972	0.75789	0.72972
0.3	0.9	0.04110	0.04110	0.04110	0.04123	0.04110
0.5	0.9	0.09091	0.09091	0.09156	0.09091	0.09091
0.7	0.9	0.18919	0.18919	0.18919	0.19194	0.18919
0.9	0.9	0.47368	0.47366	0.47368	0.48922	0.47368

ω	g	Correct ϖ	f	cos⁻¹ $μ_{0}$ (degrees)	Eq. (20)	Eq. (21)	Approximation (28)	Approximation (29)
0.3	0.7	0.11392	0.3	0	0.11392	0.11392	0.09892	0.11915
				60	0.11392	0.11392	0.10066	0.12034
0.3	0.7	0.11392	0.7	0	0.11392	0.11392	0.10647	0.11564
				60	0.11392	0.11392	0.10877	0.11684
0.3	0.9	0.04110	0.3	0	0.04109	0.04110	0.03530	0.04320
				60	0.04109	0.04110	0.03594	0.04367
0.3	0.9	0.04110	0.7	0	0.04109	0.04110	0.03807	0.04179
				60	0.04110	0.04110	0.03891	0.04226
0.5	0.7	0.23077	0.3	0	0.23076	0.23077	0.20401	0.23948
				60	0.23076	0.23077	0.20739	0.24153
0.5	0.7	0.23077	0.7	0	0.23077	0.23077	0.21878	0.23362
				60	0.23077	0.23077	0.22337	0.23569
0.5	0.9	0.09091	0.3	0	0.09090	0.09090	0.07866	0.09523
				60	0.09090	0.09091	0.08007	0.09621
0.5	0.9	0.09091	0.7	0	0.09091	0.09091	0.08473	0.09233
				60	0.09091	0.09091	0.08657	0.09331

ω	g	Correct ϖ	f	cos⁻¹ µ₀(degrees)	Eq. (20)	Eq. (21)	Approximation (28)	Approximation (29)
0.7	0.7	0.41176	0.3	0	0.41177	0.41178	0.37476	0.42249
				60	0.41176	0.41176	0.38025	0.42519
0.7	0.7	0.41176	0.7	0	0.41178	0.41178	0.39907	0.41524
				60	0.41176	0.41176	0.40709	0.41797
0.7	0.9	0.18919	0.3	0	0.18918	0.18919	0.16617	0.19687
				60	0.18918	0.18919	0.16899	0.19866
0.7	0.9	0.18919	0.7	0	0.18919	0.18919	0.17845	0.19170
				60	0.18919	0.18919	0.18223	0.19351
0.9	0.7	0.72973	0.3	0	0.72973	0.72973	0.70170	0.73610
				60	0.72972	0.72973	0.70890	0.73813
0.9	0.7	0.72973	0.7	0	0.72973	0.72973	0.73285	0.73169
				60	0.72973	0.72973	0.74698	0.73372
0.9	0.9	0.47368	0.3	0	0.47368	0.47370	0.43558	0.48425
				60	0.47368	0.47368	0.44165	0.48700
0.9	0.9	0.47368	0.7	0	0.47369	0.47369	0.46249	0.47709
				60	0.47368	0.47368	0.47168	0.47987

ω	g	Correct ϖ	Eq. (20)	Eq. (21)	Approximation (28)	Approximation (29)
0.3	0	0.3	0.29998	0.30000	0.25796	0.31672
0.5	0	0.5	0.49998	0.50000	0.44591	0.51761
0.7	0	0.7	0.69999	0.70000	0.64995	0.71228
0.9	0	0.9	0.90000	0.90000	0.87528	0.90345
0.3	0.7	0.11392	0.11391	0.11392	0.09493	0.12270
0.5	0.7	0.23077	0.23075	0.23077	0.19608	0.24540
0.7	0.7	0.41176	0.41175	0.41176	0.36121	0.42986
0.9	0.7	0.72973	0.72972	0.72973	0.68192	0.74083
0.3	0.9	0.04110	0.04109	0.04110	0.03385	0.04463
0.5	0.9	0.09091	0.09090	0.09091	0.07547	0.09816
0.7	0.9	0.18919	0.18917	0.18919	0.15963	0.20208
0.9	0.9	0.47368	0.47367	0.47368	0.42034	0.49158

Abstract

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Tables (4)

Equations (59)

Applied Optics