Accounting for the multiple-scattering effect in radiation intensities at the top of the atmosphere

A. Jayaraman; P. Koepke

doi:10.1364/AO.31.003473

Applied Optics
Vol. 31,
Issue 18,
pp. 3473-3480
(1992)
•https://doi.org/10.1364/AO.31.003473

Accounting for the multiple-scattering effect in radiation intensities at the top of the atmosphere

A. Jayaraman and P. Koepke

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A. Jayaraman and P. Koepke, "Accounting for the multiple-scattering effect in radiation intensities at the top of the atmosphere," Appl. Opt. 31, 3473-3480 (1992)

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Abstract

For obtaining aerosol optical depths over the ocean by using satellite measured radiances computations of backscattered solar radiation fields are necessary. Since a detailed multiple-scattering algorithm is time consuming a simple approach that allows parametrization of multiple-scattering processes is desired. Here the differences between multiple-scattered radiances, which are calculated by the successive order of scattering method, and single-scattered radiances, which use a simple single-scattering equation, and are obtained for different aerosol models defined as a correction term. It is shown that all correction terms could be linearly fitted with aerosol optical depths if they are scaled by the single-scattering albedo and 1 minus the asymmetry factor of the aerosol models considered. An analytic expression for the correction factor is obtained. Thus it is shown that multiple-scattered radiances at the top of the atmosphere can be estimated directly from the single-scattered radiances and with the correction term for all Sun-satellite geometries that are usually used for remote sensing of aerosol turbidities over ocean surfaces with an uncertainty of less than 10% for aerosol optical depths up to 0.5 in the visible region.

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Aerosol Model			Log Normal Size Distribution					Optical Properties

Aerosol Type	Internal Code	Relative Humidity (%)	Components	% by Number	Refrac. Index (λ = 0.55 μm)	r (μm)		ω	g	Scaling factor
Maritime (standard atmosphere, Refs. 15 and 16)	SRA00	0	1	96.397	1.530–6.60E-3	0.045	2.03	0.9944	0.7331	0.2654
			2	3.523	1.458–1.00E-8	0.274	2.03
			3	0.080	1.458–1.00E-8	2.200	2.03
	SRA70	70	1	96.397	1.501–5.63E-3	0.048	2.03	0.9959	0.7662	0.2328
			2	3.523	1.413–5.83E-9	0.333	2.03
			3	0.080	1.413–5.83E-9	2.660	2.03
	SRA95	95	1	96.397	1.384–1.71E-3	0.071	2.03	0.9988	0.7842	0.2155
			2	3.523	1.340–2.30E-9	0.628	2.03
			3	0.080	1.340–2.30E-9	5.060	2.03
Maritime (Shettle and Fenn model, Ref. 17)	SFM00	0	1	99.0	1.530–6.60E-3	0.027	2.239	0.9819	0.6804	0.3138
			2	1.0	1.500–1.00E-8	0.160	2.510
	SFM70	70	1	99.0	1.501–5.63E-3	0.028	2.239	0.9874	0.7278	0.2688
			2	1.0	1.413–5.83E-9	0.204	2.510
	SFM95	95	1	99.0	1.384–1.71E-3	0.042	2.239	0.9968	0.8016	0.1978
			2	1.0	1.340–2.30E-9	0.461	2.510
Desert dust (Ref. 19)	DES50	50	1	100.0	1.530–5.50E-2	0.500	2.200	0.8204	0.7915	0.1711

			Azimuthal Difference (φ)

∂₀	∂	100	120	140	160	180
12.5	22.5	0.120	0.120	0.121	0.121	0.121
	27.5	0.126	0.127	0.127	0.127	0.128
	32.5	0.135	0.135	0.135	0.136	0.135
	37.5	0.145	0.145	0.146	0.146	0.146
	42.5	0.158	0.158	0.158	0.159	0.159
	47.5	0.174	0.174	0.175	0.175	0.175
	52.5	0.194	0.195	0.196	0.196	0.196
	57.5	0.221	0.222	0.223	0.223	0.224
	62.5	0.257	0.258	0.258	0.259	0.259
	67.5	0.307	0.308	0.308	0.309	0.310
32.5	22.5	0.125	0.126	0.127	0.127	0.127
	27.5	0.132	0.133	0.134	0.135	0.134
	32.5	0.141	0.142	0.143	0.143	0.143
	37.5	0.151	0.152	0.153	0.154	0.156
	42.5	0.164	0.166	0.168	0.169	0.170
	47.5	0.182	0.183	0.186	0.187	0.187
	52.5	0.203	0.205	0.208	0.209	0.210
	57.5	0.231	0.233	0.236	0.238	0.239
	62.5	0.269	0.271	0.275	0.277	0.278
	67.5	0.321	0.324	0.328	0.331	0.332
52.5	00.0	0.117	0.117	0.117	0.117	0.117
	02.5	0.117	0.117	0.117	0.117	0.117
	07.5	0.119	0.119	0.119	0.119	0.119
	12.5	0.121	0.122	0.122	0.122	0.122
	17.5	0.125	0.126	0.126	0.127	0.127
	22.5	0.131	0.131	0.132	0.133	0.133
	27.5	0.138	0.139	0.140	0.141	0.141
	32.5	0.147	0.148	0.150	0.151	0.152
	37.5	0.158	0.160	0.162	0.163	0.164
	42.5	0.172	0.174	0.177	0.179	0.180
	47.5	0.190	0.192	0.195	0.199	0.199
	52.5	0.213	0.216	0.219	0.222	0.224
	57.5	0.242	0.246	0.250	0.255	0.255
	62.5	0.282	0.286	0.292	0.296	0.298
	67.5	0.338	0.343	0.349	0.355	0.357
67.5	00.0	0.116	0.116	0.116	0.116	0.116
	02.5	0.116	0.117	0.117	0.117	0.117
	07.5	0.118	0.118	0.118	0.118	0.118
	12.5	0.120	0.121	0.121	0.121	0.121
	17.5	0.124	0.125	0.125	0.126	0.126
	22.5	0.130	0.130	0.131	0.132	0.132
	27.5	0.137	0.138	0.139	0.140	0.141
	32.5	0.146	0.147	0.148	0.150	0.150
	37.5	0.157	0.159	0.161	0.163	0.164
	42.5	0.172	0.173	0.176	0.178	0.179
	47.5	0.190	0.192	0.195	0.199	0.199
	52.5	0.212	0.215	0.219	0.223	0.224
	57.5	0.242	0.246	0.251	0.255	0.257
	62.5	0.282	0.286	0.292	0.298	0.300
	67.5	0.337	0.342	0.350	0.357	0.360

			Azimuthal Difference (φ)

∂₀	∂	100	120	140	160	180
12.5	22.5	5.34	5.44	5.51	5.57	5.59
	27.5	5.58	5.66	5.76	5.83	5.85
	32.5	5.91	6.00	6.08	6.16	6.19
	37.5	6.30	6.44	6.52	6.59	6.61
	42.5	6.83	6.96	7.10	7.18	7.20
	47.5	7.53	7.68	7.79	7.91	7.95
	52.5	8.43	8.60	8.74	8.83	8.86
	57.5	9.64	9.80	9.96	10.10	10.10
	62.5	11.30	11.40	11.60	11.70	11.80
	67.5	13.50	13.60	13.80	13.90	14.00
32.5	22.5	5.47	5.63	5.80	5.94	6.00
	27.5	5.73	5.95	6.16	6.34	6.34
	32.5	6.08	6.35	6.60	6.83	6.62
	37.5	6.56	6.86	7.15	7.43	7.43
	42.5	7.16	7.48	7.82	8.14	8.27
	47.5	7.90	8.28	8.69	9.04	9.20
	52.5	8.90	9.33	9.82	10.20	10.40
	57.5	10.20	10.70	11.20	11.70	11.80
	62.5	12.00	12.40	13.10	13.70	13.40
	67.5	14.30	14.80	15.70	16.20	16.50
52.5	00.0	5.03	5.03	5.03	5.03	5.03
	02.5	5.04	5.06	5.07	5.08	5.08
	07.5	5.12	5.17	5.22	5.26	5.27
	12.5	5.24	5.35	5.44	5.49	5.50
	17.5	5.43	5.57	5.70	5.81	5.86
	22.5	5.68	5.87	6.06	6.23	6.27
	27.5	6.00	6.25	6.52	6.71	6.78
	32.5	6.41	6.72	7.07	7.33	7.45
	37.5	6.94	7.31	7.76	8.11	8.28
	42.5	7.63	8.07	8.60	9.08	9.31
	47.5	8.49	9.01	9.68	10.30	10.40
	52.5	9.61	10.20	11.00	11.80	11.60
	57.5	11.10	11.80	12.80	13.60	13.90
	62.5	13.00	13.80	15.00	16.10	16.60
	67.5	15.60	16.50	18.00	19.30	19.90
67.5	00.0	5.10	5.10	5.10	5.10	5.10
	02.5	5.11	5.12	5.12	5.12	5.12
	07.5	5.18	5.20	5.23	5.25	5.26
	12.5	5.31	5.36	5.42	5.47	5.50
	17.5	5.50	5.58	5.70	5.80	5.84
	22.5	5.75	5.88	6.06	6.22	6.28
	27.5	6.09	6.26	6.53	6.75	6.81
	32.5	6.52	6.75	7.13	7.39	7.53
	37.5	7.08	7.37	7.85	8.25	8.39
	42.5	7.79	8.16	8.76	9.28	9.44
	47.5	8.69	9.15	9.91	10.50	10.80
	52.5	9.87	10.40	11.40	12.20	12.60
	57.5	11.40	12.10	13.30	14.30	14.80
	62.5	13.40	14.20	15.70	17.10	17.50
	67.5	16.00	17.00	19.00	20.70	20.60

Aerosol Model			Log Normal Size Distribution					Optical Properties

Aerosol Type	Internal Code	Relative Humidity (%)	Components	% by Number	Refrac. Index (λ = 0.55 μm)	r (μm)		ω	g	Scaling factor
Maritime (standard atmosphere, Refs. 15 and 16)	SRA00	0	1	96.397	1.530–6.60E-3	0.045	2.03	0.9944	0.7331	0.2654
			2	3.523	1.458–1.00E-8	0.274	2.03
			3	0.080	1.458–1.00E-8	2.200	2.03
	SRA70	70	1	96.397	1.501–5.63E-3	0.048	2.03	0.9959	0.7662	0.2328
			2	3.523	1.413–5.83E-9	0.333	2.03
			3	0.080	1.413–5.83E-9	2.660	2.03
	SRA95	95	1	96.397	1.384–1.71E-3	0.071	2.03	0.9988	0.7842	0.2155
			2	3.523	1.340–2.30E-9	0.628	2.03
			3	0.080	1.340–2.30E-9	5.060	2.03
Maritime (Shettle and Fenn model, Ref. 17)	SFM00	0	1	99.0	1.530–6.60E-3	0.027	2.239	0.9819	0.6804	0.3138
			2	1.0	1.500–1.00E-8	0.160	2.510
	SFM70	70	1	99.0	1.501–5.63E-3	0.028	2.239	0.9874	0.7278	0.2688
			2	1.0	1.413–5.83E-9	0.204	2.510
	SFM95	95	1	99.0	1.384–1.71E-3	0.042	2.239	0.9968	0.8016	0.1978
			2	1.0	1.340–2.30E-9	0.461	2.510
Desert dust (Ref. 19)	DES50	50	1	100.0	1.530–5.50E-2	0.500	2.200	0.8204	0.7915	0.1711

			Azimuthal Difference (φ)

∂₀	∂	100	120	140	160	180
12.5	22.5	0.120	0.120	0.121	0.121	0.121
	27.5	0.126	0.127	0.127	0.127	0.128
	32.5	0.135	0.135	0.135	0.136	0.135
	37.5	0.145	0.145	0.146	0.146	0.146
	42.5	0.158	0.158	0.158	0.159	0.159
	47.5	0.174	0.174	0.175	0.175	0.175
	52.5	0.194	0.195	0.196	0.196	0.196
	57.5	0.221	0.222	0.223	0.223	0.224
	62.5	0.257	0.258	0.258	0.259	0.259
	67.5	0.307	0.308	0.308	0.309	0.310
32.5	22.5	0.125	0.126	0.127	0.127	0.127
	27.5	0.132	0.133	0.134	0.135	0.134
	32.5	0.141	0.142	0.143	0.143	0.143
	37.5	0.151	0.152	0.153	0.154	0.156
	42.5	0.164	0.166	0.168	0.169	0.170
	47.5	0.182	0.183	0.186	0.187	0.187
	52.5	0.203	0.205	0.208	0.209	0.210
	57.5	0.231	0.233	0.236	0.238	0.239
	62.5	0.269	0.271	0.275	0.277	0.278
	67.5	0.321	0.324	0.328	0.331	0.332
52.5	00.0	0.117	0.117	0.117	0.117	0.117
	02.5	0.117	0.117	0.117	0.117	0.117
	07.5	0.119	0.119	0.119	0.119	0.119
	12.5	0.121	0.122	0.122	0.122	0.122
	17.5	0.125	0.126	0.126	0.127	0.127
	22.5	0.131	0.131	0.132	0.133	0.133
	27.5	0.138	0.139	0.140	0.141	0.141
	32.5	0.147	0.148	0.150	0.151	0.152
	37.5	0.158	0.160	0.162	0.163	0.164
	42.5	0.172	0.174	0.177	0.179	0.180
	47.5	0.190	0.192	0.195	0.199	0.199
	52.5	0.213	0.216	0.219	0.222	0.224
	57.5	0.242	0.246	0.250	0.255	0.255
	62.5	0.282	0.286	0.292	0.296	0.298
	67.5	0.338	0.343	0.349	0.355	0.357
67.5	00.0	0.116	0.116	0.116	0.116	0.116
	02.5	0.116	0.117	0.117	0.117	0.117
	07.5	0.118	0.118	0.118	0.118	0.118
	12.5	0.120	0.121	0.121	0.121	0.121
	17.5	0.124	0.125	0.125	0.126	0.126
	22.5	0.130	0.130	0.131	0.132	0.132
	27.5	0.137	0.138	0.139	0.140	0.141
	32.5	0.146	0.147	0.148	0.150	0.150
	37.5	0.157	0.159	0.161	0.163	0.164
	42.5	0.172	0.173	0.176	0.178	0.179
	47.5	0.190	0.192	0.195	0.199	0.199
	52.5	0.212	0.215	0.219	0.223	0.224
	57.5	0.242	0.246	0.251	0.255	0.257
	62.5	0.282	0.286	0.292	0.298	0.300
	67.5	0.337	0.342	0.350	0.357	0.360

Abstract

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Tables (3)

Equations (7)

Applied Optics