Infrared Cloud Radiance

George W. Kattawar; Gilbert N. Plass

doi:10.1364/AO.8.001169

Applied Optics
Vol. 8,
Issue 6,
pp. 1169-1178
(1969)
•https://doi.org/10.1364/AO.8.001169

Infrared Cloud Radiance

George W. Kattawar and Gilbert N. Plass

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George W. Kattawar and Gilbert N. Plass, "Infrared Cloud Radiance," Appl. Opt. 8, 1169-1178 (1969)

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Abstract

The radiance of clouds is calculated at nine wavelengths in the ir. The single scattering function is obtained by Mie theory from the measured values of the complex index of refraction and with two different drop size distributions. Multiple scattering is taken into account by a Monte Carlo technique which computes the exact three-dimensional paths of the photons. The upward and downward radiance is obtained as a function of optical thickness, angle of observation, drop size distribution, and incident solar angle. The mean optical path of the photon, the cloud albedo, and the flux at the lower and upper boundaries are also given.

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Wavelength (μ)	n₁	n₂	ω₀ Nimbostratus	ω₀ Haze C
1.7	1.315	0.0000697	0.991
2.1	1.300	0.0004345	0.960
2.5	1.265	0.001651	0.888
2.75	1.188	0.019805	0.554
2.8	1.260	0.06702	0.507
2.96	1.365	0.17337	0.518	0.269
3.1	1.501	0.13800	0.526
3.5	1.423	0.00930	0.688	0.896
6.05	1.324	0.11208	0.496
11	1.151	0.1021	0.508
15	1.330	0.4298	0.474	0.0166
20	1.722	0.3899	0.481

λ (μ)	Model^a	μ₀	τ	Reflected mean optical path	Transmitted mean optical path	Flux at lower boundary, A = 0	Cloud albedo, A = 0	Upward flux at upper boundary, A = 0.8	Downward flux at lower boundary, A = 0.8
1.7	N	−1	0.1	0.482	0.113	−0.995	0.0038	0.796	−1.010
1.7	N	−1	1	3.75	1.19	−0.950	0.041	0.765	−1.052
1.7	N	−1	10	25.2	18.3	−0.513	0.340	0.594	−0.808
2.5	N	−1	0.1	0.453	0.112	−0.986	0.0026	0.772	−0.996
2.5	N	−1	1	3.74	1.14	−0.862	0.024	0.565	−0.913
2.5	N	−1	10	23.5	14.8	−0.149	0.081	0.092	−0.166
2.8	N	−1	0.1	0.655	0.106	−0.951	0.00035	0.693	−0.952
2.8	N	−1	1	4.18	1.04	−0.606	0.0019	0.216	−0.608
2.8	N	−1	10	19.8	10.5	−0.0058	0.0022	0.0022	−0.0058
2.96	N	−1	0.1	0.560	0.106	−0.952	0.00064	0.695	−0.954
2.96	N	−1	1	3.96	1.06	−0.610	0.0034	0.223	−0.614
2.96	N	−1	10	19.8	10.6	−0.0064	0.0042	0.0042	−0.0064
3.5	N	−1	0.1	0.666	0.120	−0.967	0.0017	0.729	−0.974
3.5	N	−1	1	4.26	1.16	−0.707	0.012	0.331	−0.727
3.5	N	−1	10	20.9	12.5	−0.0185	0.022	0.0226	−0.0192
6.05	N	−1	0.1	0.744	0.107	−0.950	0.00045	0.691	−0.952
6.05	N	−1	1	4.18	1.06	−0.597	0.0027	0.209	−0.601
6.05	N	−1	10	20.6	10.8	−0.0046	0.0033	0.0033	−0.0046
2.96	H	−1	0.1	0.582	0.181	−0.926	0.0025	0.646	−0.933
2.96	H	−1	1	3.59	1.56	−0.451	0.0103	0.117	−0.460
2.96	H	−1	10	11.3	12.9	−0.00014	0.0124	0.0124	−0.00015
3.5	H	−1	0.1	0.596	0.192	−0.979	0.0103	0.771	−1.009
3.5	H	−1	1	3.73	1.75	−0.773	0.0977	0.557	−0.911
3.5	H	−1	10	16.2	20.6	−0.0361	0.230	0.0230	−0.0483
1.7	N	−0.15	0.1	1.20	0.775	−0.885	0.109	0.813	−0.898
1.7	N	−0.15	1	5.35	5.49	−0.524	0.441	0.841	−0.581
1.7	N	−0.15	10	14.5	27.5	−0.199	0.685	8.783	0.312
2.8	N	−0.15	0.1	2.25	0.744	−0.693	0.0087	0.511	−0.694
2.8	N	−0.15	1	9.45	6.40	−0.0398	0.0181	0.0316	−0.400
2.8	N	−0.15	10	15.2	28.5	−0.00001	0.0177	0.0177	−0.00001

Wavelength (μ)	n₁	n₂	ω₀ Nimbostratus	ω₀ Haze C
1.7	1.315	0.0000697	0.991
2.1	1.300	0.0004345	0.960
2.5	1.265	0.001651	0.888
2.75	1.188	0.019805	0.554
2.8	1.260	0.06702	0.507
2.96	1.365	0.17337	0.518	0.269
3.1	1.501	0.13800	0.526
3.5	1.423	0.00930	0.688	0.896
6.05	1.324	0.11208	0.496
11	1.151	0.1021	0.508
15	1.330	0.4298	0.474	0.0166
20	1.722	0.3899	0.481

λ (μ)	Model^a	μ₀	τ	Reflected mean optical path	Transmitted mean optical path	Flux at lower boundary, A = 0	Cloud albedo, A = 0	Upward flux at upper boundary, A = 0.8	Downward flux at lower boundary, A = 0.8
1.7	N	−1	0.1	0.482	0.113	−0.995	0.0038	0.796	−1.010
1.7	N	−1	1	3.75	1.19	−0.950	0.041	0.765	−1.052
1.7	N	−1	10	25.2	18.3	−0.513	0.340	0.594	−0.808
2.5	N	−1	0.1	0.453	0.112	−0.986	0.0026	0.772	−0.996
2.5	N	−1	1	3.74	1.14	−0.862	0.024	0.565	−0.913
2.5	N	−1	10	23.5	14.8	−0.149	0.081	0.092	−0.166
2.8	N	−1	0.1	0.655	0.106	−0.951	0.00035	0.693	−0.952
2.8	N	−1	1	4.18	1.04	−0.606	0.0019	0.216	−0.608
2.8	N	−1	10	19.8	10.5	−0.0058	0.0022	0.0022	−0.0058
2.96	N	−1	0.1	0.560	0.106	−0.952	0.00064	0.695	−0.954
2.96	N	−1	1	3.96	1.06	−0.610	0.0034	0.223	−0.614
2.96	N	−1	10	19.8	10.6	−0.0064	0.0042	0.0042	−0.0064
3.5	N	−1	0.1	0.666	0.120	−0.967	0.0017	0.729	−0.974
3.5	N	−1	1	4.26	1.16	−0.707	0.012	0.331	−0.727
3.5	N	−1	10	20.9	12.5	−0.0185	0.022	0.0226	−0.0192
6.05	N	−1	0.1	0.744	0.107	−0.950	0.00045	0.691	−0.952
6.05	N	−1	1	4.18	1.06	−0.597	0.0027	0.209	−0.601
6.05	N	−1	10	20.6	10.8	−0.0046	0.0033	0.0033	−0.0046
2.96	H	−1	0.1	0.582	0.181	−0.926	0.0025	0.646	−0.933
2.96	H	−1	1	3.59	1.56	−0.451	0.0103	0.117	−0.460
2.96	H	−1	10	11.3	12.9	−0.00014	0.0124	0.0124	−0.00015
3.5	H	−1	0.1	0.596	0.192	−0.979	0.0103	0.771	−1.009
3.5	H	−1	1	3.73	1.75	−0.773	0.0977	0.557	−0.911
3.5	H	−1	10	16.2	20.6	−0.0361	0.230	0.0230	−0.0483
1.7	N	−0.15	0.1	1.20	0.775	−0.885	0.109	0.813	−0.898
1.7	N	−0.15	1	5.35	5.49	−0.524	0.441	0.841	−0.581
1.7	N	−0.15	10	14.5	27.5	−0.199	0.685	8.783	0.312
2.8	N	−0.15	0.1	2.25	0.744	−0.693	0.0087	0.511	−0.694
2.8	N	−0.15	1	9.45	6.40	−0.0398	0.0181	0.0316	−0.400
2.8	N	−0.15	10	15.2	28.5	−0.00001	0.0177	0.0177	−0.00001

Abstract

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Equations (1)

Applied Optics