Theoretical and numerical investigations of the intensity of the lidar signal specular reflected from a set of oriented ice plates

A. A. Popov; O. V. Shefer

doi:10.1364/AO.33.007038

Applied Optics
Vol. 33,
Issue 30,
pp. 7038-7044
(1994)
•https://doi.org/10.1364/AO.33.007038

Theoretical and numerical investigations of the intensity of the lidar signal specular reflected from a set of oriented ice plates

A. A. Popov and O. V. Shefer

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A. A. Popov and O. V. Shefer, "Theoretical and numerical investigations of the intensity of the lidar signal specular reflected from a set of oriented ice plates," Appl. Opt. 33, 7038-7044 (1994)

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Abstract

The algebraic formula of the backscattering coefficient has been derived within the scope of the physical optics method. The formula relates the lidar return anomalous high amplitude of observed experimentally with the principal parameters of a polydisperse crystalline medium. It is shown that at the lidar small-angular scanning relative to the normal to the ice-plate preferred orientation, the average size of the plate can be defined and the flutter size can be evaluated from the behavior of the lidar return variation.

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μ	ā = 37 μm, N = 0.8 L⁻¹	ā = 100 μm, N = 25 L⁻¹	ā = 150 μm N = 20 L⁻¹	ā = 200 μm N = 15 L⁻¹	ā = 250 μm N = 10 L⁻¹
1	5.22 × 10¹	8.69 × 10⁴	3.52 × 10⁵	8.35 × 10⁵	1.36 × 10⁶
2	3.09 × 10¹	5.15 × 10⁴	2.09 × 10⁵	4.95 × 10⁵	8.05 × 10⁵
3	2.28 × 10¹	3.80 × 10⁴	1.54 × 10⁵	3.65 × 10⁵	5.94 × 10⁵
4	1.87 × 10¹	3.12 × 10⁴	1.26 × 10⁵	2.99 × 10⁵	4.87 × 10⁵
5	1.62 × 10¹	2.71 × 10⁴	1.10 × 10⁵	2.60 × 10⁵	4.23 × 10⁵
6	1.46 × 10¹	2.43 × 10⁴	9.86 × 10⁴	2.34 × 10⁵	3.80 × 10⁵
7	1.46 × 10¹	2.43 × 10⁴	9.08 × 10⁴	2.15 × 10⁵	3.50 × 10⁵
8	1.26 × 10¹	2.10 × 10⁴	8.50 × 10⁴	2.02 × 10⁵	3.28 × 10⁵
9	1.19 × 10¹	1.99 × 10⁴	8.06 × 10⁴	1.91 × 10⁵	3.11 × 10⁵
10	1.14 × 10¹	1.90 × 10⁴	7.71 × 10⁴	1.83 × 10⁵	2.97 × 10⁵

β⁰	ā = 37 μm, N = 0.8 L⁻¹	ā = 100 μm, N = 25 L⁻¹	ā = 150 μm, N = 20 L⁻¹	ā = 200 μm, N = 15 L⁻¹	ā = 250 μm, N = 10 L⁻¹
λ = 0.694 μm
0	1.62 × 10¹	2.71 × 10⁴	1.10 × 10⁵	2.60 × 10⁵	4.23 × 10⁵
0.01	1.61 × 10¹	2.51 × 10⁴	9.25 × 10⁴	1.93 × 10⁵	2.68 × 10⁵
0.02	1.56 × 10¹	2.01 × 10⁴	5.75 × 10⁴	8.70 × 10⁴	8.46 × 10⁴
0.05	1.26 × 10¹	5.42 × 10³	5.82 × 10³	4.84 × 10³	3.80 × 10³
0.1	6.27	5.04 × 10²	5.65 × 10²	5.65 × 10²	4.71 × 10²
0.2	9.06 × 10⁻¹	5.89 × 10¹	7.05 × 10¹	7.04 × 10¹	5.86 × 10¹
0.5	4.46 × 10⁻²	3.75	4.49	4.49	3.74
1	5.56 × 10⁻³	4.68 × 10⁻¹	5.61 × 10⁻¹	5.61 × 10⁻¹	4.68 × 10⁻¹
2	6.93 × 10⁻⁴	5.85 × 10⁻²	7.02 × 10⁻²	7.02 × 10⁻²	5.85 × 10⁻²
5	4.45 × 10⁻⁵	3.76 × 10⁻³	4.51 × 10⁻³	4.51 × 10⁻³	3.76 × 10⁻³
λ = 10.6 μm
0	6.95 × 10⁻²	1.16 × 10²	4.70 × 10²	1.11 × 10³	1.81 × 10³
0.1	6.92 × 10⁻²	1.12 × 10²	4.37 × 10²	9.78 × 10²	1.48 × 10³
0.5	6.22 × 10⁻²	5.42 × 10¹	9.86 × 10¹	9.65 × 10¹	6.96 × 10¹
1	4.52 × 10⁻²	1.01 × 10¹	9.32	8.67	7.19
5	6.93 × 10⁻⁴	5.76 × 10⁻²	6.90 × 10⁻²	6.89 × 10⁻²	5.74 × 10⁻²
10	8.65 × 10⁻⁵	7.26 × 10⁻³	8.71 × 10⁻³	8.71 × 10⁻³	7.26 × 10⁻³
20	1.13 × 10⁻⁵	9.58 × 10⁻⁴	1.15 × 10⁻³	1.15 × 10⁻³	9.58 × 10⁻⁴
30	3.80 × 10⁻⁶	3.21 × 10⁻⁴	3.85 × 10⁻⁴	3.85 × 10⁻⁴	3.20 × 10⁻⁴

μ	ā = 37 μm, N = 0.8 L⁻¹	ā = 100 μm, N = 25 L⁻¹	ā = 150 μm N = 20 L⁻¹	ā = 200 μm N = 15 L⁻¹	ā = 250 μm N = 10 L⁻¹
1	5.22 × 10¹	8.69 × 10⁴	3.52 × 10⁵	8.35 × 10⁵	1.36 × 10⁶
2	3.09 × 10¹	5.15 × 10⁴	2.09 × 10⁵	4.95 × 10⁵	8.05 × 10⁵
3	2.28 × 10¹	3.80 × 10⁴	1.54 × 10⁵	3.65 × 10⁵	5.94 × 10⁵
4	1.87 × 10¹	3.12 × 10⁴	1.26 × 10⁵	2.99 × 10⁵	4.87 × 10⁵
5	1.62 × 10¹	2.71 × 10⁴	1.10 × 10⁵	2.60 × 10⁵	4.23 × 10⁵
6	1.46 × 10¹	2.43 × 10⁴	9.86 × 10⁴	2.34 × 10⁵	3.80 × 10⁵
7	1.46 × 10¹	2.43 × 10⁴	9.08 × 10⁴	2.15 × 10⁵	3.50 × 10⁵
8	1.26 × 10¹	2.10 × 10⁴	8.50 × 10⁴	2.02 × 10⁵	3.28 × 10⁵
9	1.19 × 10¹	1.99 × 10⁴	8.06 × 10⁴	1.91 × 10⁵	3.11 × 10⁵
10	1.14 × 10¹	1.90 × 10⁴	7.71 × 10⁴	1.83 × 10⁵	2.97 × 10⁵

β⁰	ā = 37 μm, N = 0.8 L⁻¹	ā = 100 μm, N = 25 L⁻¹	ā = 150 μm, N = 20 L⁻¹	ā = 200 μm, N = 15 L⁻¹	ā = 250 μm, N = 10 L⁻¹
λ = 0.694 μm
0	1.62 × 10¹	2.71 × 10⁴	1.10 × 10⁵	2.60 × 10⁵	4.23 × 10⁵
0.01	1.61 × 10¹	2.51 × 10⁴	9.25 × 10⁴	1.93 × 10⁵	2.68 × 10⁵
0.02	1.56 × 10¹	2.01 × 10⁴	5.75 × 10⁴	8.70 × 10⁴	8.46 × 10⁴
0.05	1.26 × 10¹	5.42 × 10³	5.82 × 10³	4.84 × 10³	3.80 × 10³
0.1	6.27	5.04 × 10²	5.65 × 10²	5.65 × 10²	4.71 × 10²
0.2	9.06 × 10⁻¹	5.89 × 10¹	7.05 × 10¹	7.04 × 10¹	5.86 × 10¹
0.5	4.46 × 10⁻²	3.75	4.49	4.49	3.74
1	5.56 × 10⁻³	4.68 × 10⁻¹	5.61 × 10⁻¹	5.61 × 10⁻¹	4.68 × 10⁻¹
2	6.93 × 10⁻⁴	5.85 × 10⁻²	7.02 × 10⁻²	7.02 × 10⁻²	5.85 × 10⁻²
5	4.45 × 10⁻⁵	3.76 × 10⁻³	4.51 × 10⁻³	4.51 × 10⁻³	3.76 × 10⁻³
λ = 10.6 μm
0	6.95 × 10⁻²	1.16 × 10²	4.70 × 10²	1.11 × 10³	1.81 × 10³
0.1	6.92 × 10⁻²	1.12 × 10²	4.37 × 10²	9.78 × 10²	1.48 × 10³
0.5	6.22 × 10⁻²	5.42 × 10¹	9.86 × 10¹	9.65 × 10¹	6.96 × 10¹
1	4.52 × 10⁻²	1.01 × 10¹	9.32	8.67	7.19
5	6.93 × 10⁻⁴	5.76 × 10⁻²	6.90 × 10⁻²	6.89 × 10⁻²	5.74 × 10⁻²
10	8.65 × 10⁻⁵	7.26 × 10⁻³	8.71 × 10⁻³	8.71 × 10⁻³	7.26 × 10⁻³
20	1.13 × 10⁻⁵	9.58 × 10⁻⁴	1.15 × 10⁻³	1.15 × 10⁻³	9.58 × 10⁻⁴
30	3.80 × 10⁻⁶	3.21 × 10⁻⁴	3.85 × 10⁻⁴	3.85 × 10⁻⁴	3.20 × 10⁻⁴

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Equations (17)

Applied Optics