The relation between the extinction coefficient of light at λ = 0.55 μm and the scattered intensity was studied as a function of the scattering angle and the wavelength, in connection with its use in the measurement of visibility with the polar nephelometer. Computations used 239 spectra of natural fogs; they considered 181 scattering angles, 22 wavelengths from 0.25 to 5 μm, three cases of polarization, and four classes of visibility. Results show that for each wavelength within the interval λ = 0.25–1.06 μm and for each polarization and visibility class, there exists a corresponding well-defined angular interval in which the above relation is linear and quite reliable. The center and the width of the angular intervals, as well as the relative standard deviation concerning the relation at hand, depend strictly on the wavelength and the class of visibility considered; they range between 26 and 56 deg, 6 and 23 deg, and 0.5 and 3.5%, respectively, so that by a proper choice of wavelength and related angular interval, visibility can be determined within 0.5%.
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Mean Value and Dispersion Coefficient of the Quantities
, σ, N, and W for the Four Classes of Spectra Used
V = 0–100 m
V = 100–200 m
V = 200–∞
V = 0–∞
Quantity
Mean
Disp.
Mean
Disp.
Mean
Disp.
Mean
Disp.
(μm)
6.22
36
6.46
33
8.2
37
7.06
38
σ (μm)
2.62
36
2.92
38
3.6
41
3.09
41
N (cm−3)
926
256
174
359
45
428
301
421
W (g m−3)
0.24
36
0.13
29
0.06
52
0.13
67
Table II
Minimum Values of the Relative Standard Deviation ∊(in %) versus λ for the Three Cases of Polarization Considered and the Fourth Class of Visibility (0 ≤ V < ∞)
λ(μm)
(∊0)min
(∊1)min
(∊2)min
0.25
0.82
0.68
0.94
0.3
0.58
0.51
0.65
0.3472
0.80
0.85
0.74
0.40
0.56
0.64
0.57
0.45
0.75
0.61
0.92
0.4880
0.86
0.63
1.15
0.55
1.31
0.93
1.74
0.6
1.82
1.53
2.15
0.6328
2.38
2.26
2.55
0.6943
2.29
2.16
2.47
0.75
1.87
1.79
2.00
0.8
1.69
1.79
1.72
0.85
1.60
1.82
1.55
0.9
1.85
2.20
1.64
1.06
2.75
3.54
2.19
1.2
3.04
4.01
2.53
1.4
4.11
5.40
3.39
1.6
4.04
4.55
3.98
2
8.55
8.02
9.22
2.4
12.60
11.60
13.60
3.5
22.80
20.20
25.40
5
19.90
18.60
21.30
Table III
Lower and Upper Limits (θ1, θ2) of the θ Intervals with Low Relative Standard Deviation versus λ for the First Class of Visibility (V = 0–100 m)a
λ(μm)
θ1
θ2
θ1
θ2
θ1
θ2
0.25
52
59
0.95
3.17
50
59
0.81
3.37
53
59
1.12
2.91
0.3
46
53
0.86
2.09
43
53
0.99
2.13
47
53
0.85
1.95
0.3472
41
49
0.60
1.54
41
49
0.58
1.69
42
49
0.59
1.45
0.4
36
46
0.63
1.17
36
46
0.81
1.27
36
46
0.62
1.09
0.45
20
35
0.98
0.50
18
36
1.36
0.51
21
35
0.79
0.49
0.4880
27
37
0.68
0.64
25
37
0.90
0.64
29
37
0.84
0.65
0.55
34
43
1.19
0.98
33
43
1.06
1.02
35
43
1.60
0.95
0.6
38
47
1.62
1.29
36
47
1.46
1.32
38
48
2.06
1.24
0.6328
32
49
2.17
1.17
30
49
1.85
1.20
40
49
2.25
1.36
0.6943
33
51
2.32
1.30
32
51
2.08
1.38
35
51
2.52
1.27
0.75
36
44
1.76
1.07
34
44
1.63
1.08
37
45
2.01
1.07
0.8
37
47
1.75
1.24
36
46
1.64
1.25
39
48
1.80
1.27
0.85
40
49
1.60
1.46
40
48
1.52
1.53
40
51
1.73
1.45
0.9
40
52
1.93
1.65
40
50
1.91
1.66
40
53
1.91
1.57
1.06
41
57
2.82
2.05
44
57
3.45
2.47
40
55
2.35
1.69
and
are mean relative standard deviations and mean regression coefficients concerning the σe(0.55 μm) − I0,1,2(λ, θ) relations for the three cases of polarization considered. Angles are in degrees, standard deviations in percent. The coefficients
, and
are in m−1 (cm sr) × 103; before use divide them by 103.
Table IV
Lower and Upper Limits (θ1, θ2) of the θ Intervals with Low Relative Standard Deviation versus λ for the Second Class of Visibility (V = 100–200 m)a
Mean Value and Dispersion Coefficient of the Quantities
, σ, N, and W for the Four Classes of Spectra Used
V = 0–100 m
V = 100–200 m
V = 200–∞
V = 0–∞
Quantity
Mean
Disp.
Mean
Disp.
Mean
Disp.
Mean
Disp.
(μm)
6.22
36
6.46
33
8.2
37
7.06
38
σ (μm)
2.62
36
2.92
38
3.6
41
3.09
41
N (cm−3)
926
256
174
359
45
428
301
421
W (g m−3)
0.24
36
0.13
29
0.06
52
0.13
67
Table II
Minimum Values of the Relative Standard Deviation ∊(in %) versus λ for the Three Cases of Polarization Considered and the Fourth Class of Visibility (0 ≤ V < ∞)
λ(μm)
(∊0)min
(∊1)min
(∊2)min
0.25
0.82
0.68
0.94
0.3
0.58
0.51
0.65
0.3472
0.80
0.85
0.74
0.40
0.56
0.64
0.57
0.45
0.75
0.61
0.92
0.4880
0.86
0.63
1.15
0.55
1.31
0.93
1.74
0.6
1.82
1.53
2.15
0.6328
2.38
2.26
2.55
0.6943
2.29
2.16
2.47
0.75
1.87
1.79
2.00
0.8
1.69
1.79
1.72
0.85
1.60
1.82
1.55
0.9
1.85
2.20
1.64
1.06
2.75
3.54
2.19
1.2
3.04
4.01
2.53
1.4
4.11
5.40
3.39
1.6
4.04
4.55
3.98
2
8.55
8.02
9.22
2.4
12.60
11.60
13.60
3.5
22.80
20.20
25.40
5
19.90
18.60
21.30
Table III
Lower and Upper Limits (θ1, θ2) of the θ Intervals with Low Relative Standard Deviation versus λ for the First Class of Visibility (V = 0–100 m)a
λ(μm)
θ1
θ2
θ1
θ2
θ1
θ2
0.25
52
59
0.95
3.17
50
59
0.81
3.37
53
59
1.12
2.91
0.3
46
53
0.86
2.09
43
53
0.99
2.13
47
53
0.85
1.95
0.3472
41
49
0.60
1.54
41
49
0.58
1.69
42
49
0.59
1.45
0.4
36
46
0.63
1.17
36
46
0.81
1.27
36
46
0.62
1.09
0.45
20
35
0.98
0.50
18
36
1.36
0.51
21
35
0.79
0.49
0.4880
27
37
0.68
0.64
25
37
0.90
0.64
29
37
0.84
0.65
0.55
34
43
1.19
0.98
33
43
1.06
1.02
35
43
1.60
0.95
0.6
38
47
1.62
1.29
36
47
1.46
1.32
38
48
2.06
1.24
0.6328
32
49
2.17
1.17
30
49
1.85
1.20
40
49
2.25
1.36
0.6943
33
51
2.32
1.30
32
51
2.08
1.38
35
51
2.52
1.27
0.75
36
44
1.76
1.07
34
44
1.63
1.08
37
45
2.01
1.07
0.8
37
47
1.75
1.24
36
46
1.64
1.25
39
48
1.80
1.27
0.85
40
49
1.60
1.46
40
48
1.52
1.53
40
51
1.73
1.45
0.9
40
52
1.93
1.65
40
50
1.91
1.66
40
53
1.91
1.57
1.06
41
57
2.82
2.05
44
57
3.45
2.47
40
55
2.35
1.69
and
are mean relative standard deviations and mean regression coefficients concerning the σe(0.55 μm) − I0,1,2(λ, θ) relations for the three cases of polarization considered. Angles are in degrees, standard deviations in percent. The coefficients
, and
are in m−1 (cm sr) × 103; before use divide them by 103.
Table IV
Lower and Upper Limits (θ1, θ2) of the θ Intervals with Low Relative Standard Deviation versus λ for the Second Class of Visibility (V = 100–200 m)a