Parameters for Attenuation in the Atmospheric Windows for Fifteen Wavelengths

Louis Elterman

doi:10.1364/AO.3.000745

Applied Optics
Vol. 3,
Issue 6,
pp. 745-749
(1964)
•https://doi.org/10.1364/AO.3.000745

Parameters for Attenuation in the Atmospheric Windows for Fifteen Wavelengths

Louis Elterman

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Louis Elterman, "Parameters for Attenuation in the Atmospheric Windows for Fifteen Wavelengths," Appl. Opt. 3, 745-749 (1964)

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Abstract

A model of a Clear Standard Atmosphere for determining attenuation in the visible and infrared windows is useful for the interpretation of the optical properties of the atmosphere. It can be used, like the U.S. Standard Atmosphere, as an information source for many technical requirements. First, a Clear Standard Atmosphere is defined. A model is then derived based on a molecular atmosphere with an aerosol component determined by sea level and high-altitude measurements. The format of the model is a series of tabulations for fifteen wavelengths from 0.4 μ to 4.0 μ with molecular and aerosol parameters arrayed at kilometer intervals to an altitude of 30 km. Horizontal, vertical, and slant path transmission from sea level, transmission between two altitudes, and transmission to space are readily calculated from the model. A sample tabulation for 0.55 μ is presented. Tabulations for the other wavelengths are contained in ref. 17 [ L. Elterman, Rept. AFCRL-63-675 ( July 1963)].

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λ (μ)	β_p(0) (km⁻¹)
0.40	0.200
0.45	0.180
0.50	0.167
0.55	0.158
0.60	0.150
0.65	0.142
0.70	0.135
0.80	0.127
0.90	0.120
1.06	0.113
1.26	0.108
1.67	0.098
2.17	0.085
3.50	0.070
4.00	0.063

h (km)	Aerosol density (cm⁻³)	Source
0	2.0 × 10²	ref. 9

1	8.7 × 10¹
2	3.8 × 10¹	Scale height 1.2 km, ref. 14
3	1.6 × 10¹
4	7.2 × 10⁰
5	3.1 × 10⁰

6	1.1 × 10⁰
7	4.0 × 10⁻¹
8	1.4 × 10⁻¹	Interpolation
9	5.0 × 10⁻²
10	2.6

11	2.3
12	2.1
13	2.3
14	2.5
15	4.1
16	6.7
17	7.3
18	8.0	ref. 13
19	9.0
20	8.6
21	8.2
22	8.0
23	7.6
24	5.2
25	3.6
26	2.5
27	2.4
28	2.2

29	2.0
30	1.9	Extrapolation

1	2	3	4	5	6	7	8
h	β_r	τ_r	τ_r^′	β_p	β_t	τ_t	τ_t^′

λ (μ)	σ_r (cm²)
0.40	1.689 × 10⁻²⁶
0.45	1.038
0.50	6.735 × 10⁻²⁷
0.55	4.563
0.60	3.202
0.65	2.313
0.70	1.713
0.80	9.989 × 10⁻²⁸
0.90	6.212
1.06	3.320
1.26	1.600
1.67	5.210 × 10⁻²⁹
2.17	1.800
3.50	2.681 × 10⁻³⁰
4.00	1.571

h (km)	N_r (cm⁻³)
0	2.5476 × 10¹⁹
1	2.3118
2	2.0933
3	1.8909
4	1.7039
5	1.5315
6	1.3728
7	1.2270
8	1.0934
9	9.7130 × 10¹⁸
10	8.5993
11	7.5864
12	6.4870
13	5.5441
14	4.7385
15	4.0501
16	3.4619
17	2.9593
18	2.5298
19	2.1627
20	1.8487
21	1.5743
22	1.3414
23	1.1437
24	9.7598 × 10¹⁷
25	8.3346
26	7.1230
27	6.0920
28	5.2141
29	4.4660
30	3.8480

Alt. (km) h	Rayleigh atten. coeff. (km⁻¹) β_r	Rayleigh opt. thick. (0 − h) τ_r	Rayleigh opt. thick. (h − ∞) τ_r^′	Aerosol atten. coeff. (km⁻¹) β_p	Total atten. coeff. (km⁻¹) β_t	Turbid opt. thick. (0 − h) τ_t	Turbid opt. thick. (h − ∞) τ_t^′
0	1.162-002	0.0000	0.0926	1.58-001	1.70-001	0.0000	0.2151
1	1.055-002	0.0105	0.0820	6.95-002	8.01-002	0.0801	0.1350
2	9.552-003	0.0201	0.0725	3.00-002	3.96-002	0.1196	0.0954
3	8.628-003	0.0287	0.0638	1.26-002	2.13-002	0.1409	0.0742
4	7.775-003	0.0365	0.0561	5.69-003	1.35-002	0.1544	0.0607
5	6.988-003	0.0435	0.0491	2.53-003	9.52-003	0.1639	0.0512
6	6.264-003	0.0498	0.0428	8.69-004	7.13-003	0.1710	0.0441
7	5.599-003	0.0554	0.0372	3.16-004	5.91-003	0.1769	0.0381
8	4.989-003	0.0603	0.0322	1.11-004	5.10-003	0.1820	0.0330
9	4.432-003	0.0648	0.0278	3.95-005	4.47-003	0.1865	0.0286
10	3.924-003	0.0687	0.0239	2.05-005	3.94-003	0.1905	0.0246
11	3.462-003	0.0722	0.0204	1.90-005	3.48-003	0.1939	0.0211
12	2.960-003	0.0751	0.0174	1.74-005	2.98-003	0.1969	0.0182
13	2.530-003	0.0777	0.0149	1.90-005	2.55-003	0.1995	0.0156
14	2.162-003	0.0798	0.0127	2.05-005	2.18-003	0.2016	0.0134
15	1.848-003	0.0817	0.0109	3.32-005	1.88-003	0.2035	0.0116
16	1.580-003	0.0832	0.0093	5.37-005	1.63-003	0.2052	0.0099
17	1.350-003	0.0846	0.0080	5.85-005	1.41-003	0.2066	0.0085
18	1.154-003	0.0857	0.0068	6.32-005	1.22-003	0.2078	0.0073
19	9.868-004	0.0867	0.0058	7.11-005	1.06-003	0.2088	0.0062
20	8.436-004	0.0876	0.0050	6.79-005	9.12-004	0.2098	0.0053
21	7.184-004	0.0883	0.0043	6.48-005	7.83-004	0.2105	0.0045
22	6.121-004	0.0889	0.0037	6.32-005	6.75-004	0.2112	0.0039
23	5.219-004	0.0894	0.0031	6.00-005	5.82-004	0.2118	0.0033
24	4.453-004	0.0899	0.0027	4.11-005	4.86-004	0.2123	0.0028
25	3.803-004	0.0903	0.0023	2.84-005	4.09-004	0.2127	0.0024
26	3.250-004	0.0906	0.0020	2.05-005	3.46-004	0.2130	0.0020
27	2.780-004	0.0909	0.0017	1.90-005	2.97-004	0.2133	0.0018
28	2.379-004	0.0911	0.0015	1.74-005	2.55-004	0.2136	0.0015
29	2.038-004	0.0913	0.0013	1.58-005	2.20-004	0.2138	0.0013
30	1.747-004	0.0915	0.0011	1.50-005	1.90-004	0.2140	0.0011

Abstract

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Applied Optics