RamBackscattering, extinction, and liquid water content in fog: a detailed study of their relations for use in lidar systems

Glauco Tonna

doi:10.1364/AO.30.001132

Applied Optics
Vol. 30,
Issue 9,
pp. 1132-1140
(1991)
•https://doi.org/10.1364/AO.30.001132

RamBackscattering, extinction, and liquid water content in fog: a detailed study of their relations for use in lidar systems

Glauco Tonna

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Glauco Tonna, "RamBackscattering, extinction, and liquid water content in fog: a detailed study of their relations for use in lidar systems," Appl. Opt. 30, 1132-1140 (1991)

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Abstract

A solution to the single-scattering lidar equation to infer optical extinction, liquid water content W, and visibility in a fog through a monostatic pulsed lidar, requires the use of the relations, and combinations of them, between backscattering coefficient β, extinction coefficient σ, and W. To this end, β and σ have been computed for 239 droplet size spectra and forty wavelengths from 0.25 to 12 μm, together with W, and the three relations β vs σ, W vs σ, and σ(0.55 μm) vs σ have been determined. The analysis of their behavior with wavelength shows that (1) the relation β vs σ is mostly reliable in the λ = 0.25–2-μm region, where the dispersion of the β values around the best-fit curve is within 20%; (2) the relation W vs σ is generally not well verified (the dispersion is centered around 30%), and when used in connection with the β vs σ relation to infer liquid water content, their joint dispersion P_D is always greater than 20%; (3) the relation σ(0.55 μm) vs σ is well verified in the region λ = 0.25–2 μm (dispersion within 15%), and when used in connection with the β vs σ relation to infer visibility P_D appears to be minimum at λ ≅ 0.35 μm (P_D = 4.7%).

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λ(μm)	CORR1	DISP1	c₁· 10²	K1
0.2500	0.991	9.45	5.649	1.026
0.3472	0.999	3.49	5.139	0.992
0.4880	0.981	12.94	4.214	0.940
0.5140	0.977	14.18	4.052	0.929
0.5320	0.975	14.80	4.021	0.926
0.5500	0.972	15.80	3.844	0.918
0.6328	0.965	17.56	3.598	0.900
0.6943	0.961	18.70	3.486	0.897
0.7250	0.957	19.42	3.499	0.893
0.8000	0.956	19.70	3.441	0.890
0.9000	0.958	19.37	3.718	0.907
1.0600	0.962	18.25	3.584	0.903
1.4000	0.976	14.78	3.824	0.949
1.6000	0.976	14.58	4.154	0.957
2.0000	0.959	20.48	3.753	1.010

λ(μm)	CORR2	DISP2	c₂	K2	P_C	P_D
0.2500	0.880	32.49	3.876	0.877	0.937	23.92
0.3472	0.879	3239	3.864	0.878	0.941	23.18
0.4880	0.862	34.62	3.304	0.838	0.923	26.13
0.5140	0.859	35.02	3.203	0.830	0.920	26.71
0.3320	0.856	35.29	3.140	0.825	0.917	27.06
0.3500	0.854	35.32	3.080	0.820	0.915	27.49
0.6328	0.848	36.16	2.915	0.806	0.908	28.42
0.6943	0.847	36.29	2.876	0.803	0.906	28.86
0.7250	0.848	36.24	2.879	0.804	0.904	29.07
0.8000	0.849	36.12	2.911	0.808	0.904	29.09
0.9000	0.853	35.67	2.999	0.817	0.907	28.70
1.0600	0.863	34.36	3.223	0.838	0.914	27.63
1.4000	0.882	32.16	3.765	0.883	0.930	25.03
1.6000	0.891	30.95	4.028	0.903	0.935	24.19
2.0000	0.901	29.37	4.311	0.925	0.931	25.44
2.4000	0.906	28.87	4.343	0.944	0.932	25.35
2.8500	0.919	26.89	5.011	0.954	0.917	28.28
3.0000	0.900	29.76	4.307	0.926	0.919	27.36
3.2500	0.902	29.33	4.280	0.931	0.872	37.26
3.3000	0.904	29.15	4.388	0.942	0.930	25.94
3.7500	0.903	29.40	4.356	0.943	0.922	27.83
4.0000	0.901	29.61	4.332	0.945	0.912	30.01
4.3000	0.895	30.44	4.076	0.935	0.902	31.63
5.0000	0.887	31.60	3.703	0.915	0.881	34.73
5.3000	0.880	32.46	3.272	0.889	0.851	38.13
5.8000	0.900	29.79	3.470	0.903	0.912	27.81
6.0000	0.919	26.93	4.256	0.939	0.907	29.48
6.3000	0.895	30.48	3.672	0.916	0.931	25.07
6.3000	0.891	31.02	3.438	0.903	0.919	26.90
7.0000	0.896	30.32	3.284	0.895	0.912	27.85
7.3000	0.907	28.83	3.313	0.898	0.916	27.10
8.0000	0.920	26.80	3.421	0.904	0.924	25.93
8.6000	0.938	23.76	3.689	0.917	0.925	25.96
9.0000	0.950	21.23	3.971	0.928	0.923	26.66
9.6000	0.969	16.92	4.390	0.946	0.920	28.09
10.0000	0.980	13.65	5.250	0.959	0.917	28.49
10.6000	0.989	10.32	6.787	0.979	0.926	26.26
11.0000	0.988	10.61	7.780	0.989	0.943	22.82
11.3000	0.981	13.23	8.175	0.995	0.960	19.01
12.0000	0.972	15.94	7.671	0.993	0.967	17.34

λ(μm)	CORL3	DISPL3	a₃	P_C	P_D
0.2500	0.997	5.75	1.035	0.994	7.78
0.3472	0.997	5.75	1.028	0.998	4.69
0.4880	1.000	1.81	1.009	0.991	9.23
0.5140	1.000	1.03	1.005	0.989	10.05
0.5320	1.000	0.48	1.002	0.988	10.47
0.5500	1.000	0.00	1.000	0.986	11.17
0.6328	1.000	1.50	0.992	0.983	12.46
0.6943	1.000	1.91	0.988	0.981	13.28
0.7250	1.000	1.92	0.985	0.979	13.79
0.8000	1.000	1.96	0.982	0.978	14.00
0.9000	1.000	2.08	0.980	0.979	13.77
1.0600	0.999	3.39	0.979	0.981	13.13
1.4000	0.993	8.35	0.976	0.985	11.99
1.6000	0.987	11.08	0.973	0.982	12.93
2.0000	0.975	15.43	0.961	0.967	18.13
2.4000	0.960	19.41	0.944	0.959	20.60
2.8500	0.965	18.19	1.008	0.940	24.56
3.0000	0.981	13.57	0.958	0.960	20.21

λ(μm)	CORR1	DISP1	c₁· 10²	K1
0.2500	0.991	9.45	5.649	1.026
0.3472	0.999	3.49	5.139	0.992
0.4880	0.981	12.94	4.214	0.940
0.5140	0.977	14.18	4.052	0.929
0.5320	0.975	14.80	4.021	0.926
0.5500	0.972	15.80	3.844	0.918
0.6328	0.965	17.56	3.598	0.900
0.6943	0.961	18.70	3.486	0.897
0.7250	0.957	19.42	3.499	0.893
0.8000	0.956	19.70	3.441	0.890
0.9000	0.958	19.37	3.718	0.907
1.0600	0.962	18.25	3.584	0.903
1.4000	0.976	14.78	3.824	0.949
1.6000	0.976	14.58	4.154	0.957
2.0000	0.959	20.48	3.753	1.010

λ(μm)	CORR2	DISP2	c₂	K2	P_C	P_D
0.2500	0.880	32.49	3.876	0.877	0.937	23.92
0.3472	0.879	3239	3.864	0.878	0.941	23.18
0.4880	0.862	34.62	3.304	0.838	0.923	26.13
0.5140	0.859	35.02	3.203	0.830	0.920	26.71
0.3320	0.856	35.29	3.140	0.825	0.917	27.06
0.3500	0.854	35.32	3.080	0.820	0.915	27.49
0.6328	0.848	36.16	2.915	0.806	0.908	28.42
0.6943	0.847	36.29	2.876	0.803	0.906	28.86
0.7250	0.848	36.24	2.879	0.804	0.904	29.07
0.8000	0.849	36.12	2.911	0.808	0.904	29.09
0.9000	0.853	35.67	2.999	0.817	0.907	28.70
1.0600	0.863	34.36	3.223	0.838	0.914	27.63
1.4000	0.882	32.16	3.765	0.883	0.930	25.03
1.6000	0.891	30.95	4.028	0.903	0.935	24.19
2.0000	0.901	29.37	4.311	0.925	0.931	25.44
2.4000	0.906	28.87	4.343	0.944	0.932	25.35
2.8500	0.919	26.89	5.011	0.954	0.917	28.28
3.0000	0.900	29.76	4.307	0.926	0.919	27.36
3.2500	0.902	29.33	4.280	0.931	0.872	37.26
3.3000	0.904	29.15	4.388	0.942	0.930	25.94
3.7500	0.903	29.40	4.356	0.943	0.922	27.83
4.0000	0.901	29.61	4.332	0.945	0.912	30.01
4.3000	0.895	30.44	4.076	0.935	0.902	31.63
5.0000	0.887	31.60	3.703	0.915	0.881	34.73
5.3000	0.880	32.46	3.272	0.889	0.851	38.13
5.8000	0.900	29.79	3.470	0.903	0.912	27.81
6.0000	0.919	26.93	4.256	0.939	0.907	29.48
6.3000	0.895	30.48	3.672	0.916	0.931	25.07
6.3000	0.891	31.02	3.438	0.903	0.919	26.90
7.0000	0.896	30.32	3.284	0.895	0.912	27.85
7.3000	0.907	28.83	3.313	0.898	0.916	27.10
8.0000	0.920	26.80	3.421	0.904	0.924	25.93
8.6000	0.938	23.76	3.689	0.917	0.925	25.96
9.0000	0.950	21.23	3.971	0.928	0.923	26.66
9.6000	0.969	16.92	4.390	0.946	0.920	28.09
10.0000	0.980	13.65	5.250	0.959	0.917	28.49
10.6000	0.989	10.32	6.787	0.979	0.926	26.26
11.0000	0.988	10.61	7.780	0.989	0.943	22.82
11.3000	0.981	13.23	8.175	0.995	0.960	19.01
12.0000	0.972	15.94	7.671	0.993	0.967	17.34

Abstract

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Figures (10)

Tables (3)

Equations (9)

Applied Optics