The Backscattering and Extinction of Visible and Infrared Radiation by Selected Major Cloud Models

L. W. Carrier; G. A. Cato; K. J. von Essen

doi:10.1364/AO.6.001209

Applied Optics
Vol. 6,
Issue 7,
pp. 1209-1216
(1967)
•https://doi.org/10.1364/AO.6.001209

The Backscattering and Extinction of Visible and Infrared Radiation by Selected Major Cloud Models

L. W. Carrier, G. A. Cato, and K. J. von Essen

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L. W. Carrier, G. A. Cato, and K. J. von Essen, "The Backscattering and Extinction of Visible and Infrared Radiation by Selected Major Cloud Models," Appl. Opt. 6, 1209-1216 (1967)

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Abstract

Volume backscattering functions and optical extinction coefficients are computed for eight suggested major cloud models using the Mie theory for optical wavelengths of 0.488 μ, 0.694 μ, 1.06 μ, 4.0 μ, and 10.6 μ. Results show that there is no clear advantage of one wavelength over another for improving cloud transmission; however, backscattering is significantly reduced at the longer wavelengths. Variations in the optical properties of clouds are also discussed and calculations summarized to indicate the effects of cloud thickness, inhomogeneity, and geographical location on the backscatter function and extinction coefficient.

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Cloud type	N^a (No./cm³)	r_mode (μ)	r_min (μ)	r_max (μ)	Δr (μ)
Stratus I	464	3.5	0	16.0	3.0
Altostratus	450	4.5	0	13.0	4.5
Stratocumulus	350	3.5	0	11.2	4.4
Nimbostratus	330	3.5	0	19.8	9.5
Fair-weather cumulus	300	3.5	0.5	10.0	3.0
Stratus II	260	4.5	0	20.0	5.7
Cumulus congestus	207	3.5	0	16.2	6.7
Cumulonimbus	72	5.0	0	30.0	7.0

Scattering Function (m⁻¹sr⁻¹)

	Wavelength

Cloud type	0.488 μ	0.694 μ	1.06 μ	4.0 μ	10.6 μ
Nimbostratus	7.16 × 10⁻³	6.03 × 10⁻³	6.45 × 10⁻³	3.96 × 10⁻³	1.54 × 10⁻⁴
Altostratus	6.77 × 10⁻³	4.52 × 10⁻³	4.99 × 10⁻³	3.20 × 10⁻³	1.25 × 10⁻⁴
Stratus II	6.04 × 10⁻³	4.76 × 10⁻³	4.62 × 10⁻³	2.87 × 10⁻³	1.31 × 10⁻⁴
Cumulus congestus	3.97 × 10⁻³	3.01 × 10⁻³	3.66 × 10⁻³	2.43 × 10⁻³	7.88 × 10⁻⁵
Stratus I	3.13 × 10⁻³	2.88 × 10⁻³	3.08 × 10⁻³	1.47 × 10⁻³	7.42 × 10⁻⁵
Cumulonimbus	2.40 × 10⁻³	2.21 × 10⁻³	2.19 × 10⁻³	9.13 × 10⁻⁴	1.16 × 10⁻⁴
Stratocumulus	2.44 × 10⁻³	1.91 × 10⁻³	2.08 × 10⁻³	8.91 × 10⁻⁴	5.95 × 10⁻⁵
Fair Wx cumulus	1.18 × 10⁻³	8.68 × 10⁻⁴	1.00 × 10⁻³	4.17 × 10⁻⁴	2.31 × 10⁻⁵

Optical Extinction b (m⁻¹)

	Wavelength

Cloud type	0.488 μ	0.694 μ	1.06 μ	4.0 μ	10.6 μ
Nimbostratus	1.28 × 10⁻¹	1.30 × 10⁻¹	1.32 × 10⁻¹	1.47 × 10⁻¹	1.36 × 10⁻¹
Altostratus	1.08 × 10⁻¹	1.09 × 10⁻¹	1.12 × 10⁻¹	1.30 × 10⁻¹	8.39 × 10⁻²
Stratus II	1.00 × 10⁻¹	1.01 × 10⁻¹	1.03 × 10⁻¹	1.14 × 10⁻¹	1.04 × 10⁻¹
Cumulus congestus	6.92 × 10⁻²	6.98 × 10⁻²	7.13 × 10⁻²	8.10 × 10⁻²	6.76 × 10⁻²
Stratus I	6.69 × 10⁻²	6.79 × 10⁻²	6.97 × 10⁻²	9.01 × 10⁻²	4.28 × 10⁻²
Cumulonimbus	4.35 × 10⁻²	4.38 × 10⁻²	4.44 × 10⁻²	4.82 × 10⁻²	5.09 × 10⁻²
Stratocumulus	4.53 × 10⁻²	4.60 × 10⁻²	4.71 × 10⁻²	5.96 × 10⁻²	2.48 × 10⁻²
Fair Wx cumulus	2.10 × 10⁻²	2.13 × 10⁻²	2.19 × 10⁻²	2.76 × 10⁻²	1.17 × 10⁻²

Cloud type sample height (m)	β(π) (m⁻¹sr⁻¹)	b (m⁻¹)	N (cm⁻³)	r_mode (μ)	r_min (μ)	r_max (μ)	Δr (μ)
Cumulus
1. 1035	1.36 × 10⁻³	2.78 × 10⁻²	64	4.5	0	12.8	6.4
2. 1035	8.37 × 10⁻³	1.67 × 10⁻²	145	1.5	0	10.8	2.8
3. 1035^b	4.38 × 10⁻³	9.13 × 10⁻²	173	4.5	0	16.0	5.4

Cloud type and thickness (m)	β(π) (m⁻¹sr⁻¹)	b (m⁻¹)	N (cm⁻³)	r_mode (μ)	r_min (μ)	r_max (ν)	Δr (μ)
Stratus^a
1. 213–305	1.98 × 10⁻³	4.22 × 10⁻²	133	4.5	0	27.5	4.4
2. 610	2.43 × 10⁻³	4.93 × 10⁻²	63	4.8	1.2	42.2	4.6
3. 1975–2130	3.34 × 10⁻³	6.04 × 10⁻²	40	5.0	0	60.8	8.0
Note 1	1.35 × 10⁻³	2.83 × 10⁻²	36	—	0	25.0	—
Note 2	3.01 × 10⁻³	5.38 × 10⁻²	12	—	10	60.8	—
Cumulus^b
1. 230–765	2.80 × 10⁻³	6.00 × 10⁻²	211	4.0	0	19.8	4.0
2. 1175–2130	6.23 × 10⁻³	1.27 × 10⁻¹	206	4.0	0	30.2	7.2

Trade-Wind Cumulus off the East Coast of Hawaii (Base = 670 m Top = 2900 m)

Sample height	β(π) (m⁻¹sr⁻¹)	b (m⁻¹)	N (cm⁻³)	r_mode (μ)	r_min (μ)	r_max (μ)	Δr (μ)
1. 990	1.94 × 10⁻²	3.77 × 10⁻¹	74	10	0	25	8.5
2. 1300	1.48 × 10⁻²	2.92 × 10⁻¹	51	15	0	23.2	8.5
3. 1600	1.43 × 10⁻²	2.99 × 10⁻¹	27	17.5	0	32.2	12.5
4. 1900	1.37 × 10⁻²	2.77 × 10⁻¹	30	10.0	0	34.8	16.0

Continental Cumulus over the Blue Mountains Northwest of Sydney, Australia (Base = 2200 m Top = 3660 m)

Sample height (m)	β(π) (m⁻¹sr⁻¹)	b (m⁻¹)	N (cm⁻³)	r_mode (μ)	r_min (μ)	r_max (μ)	Δr (μ)
1. 2500	7.15 × 10⁻³	1.78 × 10⁻¹	490	5.5	0	12.2	3.0
2. 2775	6.84 × 10⁻³	1.48 × 10⁻¹	270	7.0	0	11.5	3.5
3. 3000	8.68 × 10⁻³	1.64 × 10⁻¹	250	7.5	0	11.5	2.0
4. 3420	1.34 × 10⁻²	2.47 × 10⁻¹	350	7.5	0	13.0	2.0

Cloud type and location	β (π) (m⁻¹sr⁻¹)	b (m⁻¹)	N (cm⁻³)	r_mode (μ)	r_min (μ)	r_max (μ)	Δr (μ)
Cumulus and Cumulonimbus
1. Pacific Coast of USA	5.94 × 10⁻³	1.20 × 10⁻¹	90	9	0	17.2	7.6
2. Other parts of USA	8.71 × 10⁻³	1.74 × 10⁻¹	160	7.5	0	16.0	6.3
Stratus and Stratocumulus
1. Pacific Coast of USA	4.88 × 10⁻³	1.00 × 10⁻¹	100	5	1.2	16.5	6
2. Other parts of USA	8.70 × 10⁻³	1.89 × 10⁻¹	320	5.5	0	15.5	4.7
Altocumulus and Altostratus
1. Pacific Coast of USA	1.99 × 10⁻³	3.90 × 10⁻²	35	7.5	0.8	16.0	6.2
2. Other parts of USA	3.47 × 10⁻³	6.90 × 10⁻²	75	6.0	0	17.0	7

Abstract

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Applied Optics