Relationship between backscattering and extinction coefficients of aerosols with application to turbid atmosphere

K. Parameswaran; K. O. Rose; B. V. Krishna Murthy

doi:10.1364/AO.30.003059

Applied Optics
Vol. 30,
Issue 21,
pp. 3059-3071
(1991)
•https://doi.org/10.1364/AO.30.003059

Relationship between backscattering and extinction coefficients of aerosols with application to turbid atmosphere

K. Parameswaran, K. O. Rose, and B. V. Krishna Murthy

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K. Parameswaran, K. O. Rose, and B. V. Krishna Murthy, "Relationship between backscattering and extinction coefficients of aerosols with application to turbid atmosphere," Appl. Opt. 30, 3059-3071 (1991)

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Abstract

The relationship between backscattering β_a, and extinction α_a coefficients of aerosols at a ruby laser wavelength of 694.3 nm is studied using Mie scattering theory. A simple relationship of the form $β_{a} = C_{a} α_{a}^{k a}$ is assumed, and the dependence of k_a and C_a on different aerosol characteristics such as size distribution and refractive index is studied. The validity of a similar relationship is examined for a turbid atmosphere (troposphere and lower stratosphere) containing both aerosols and air molecules.

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Corrections

K. Parameswaran, K. O. Rose, and B. V. Krishna Murthy, "Relationship between backscattering and extinction coefficients of aerosols with application to turbid atmosphere: erratum," Appl. Opt. 31, 1920-1920 (1992)
https://opg.optica.org/ao/abstract.cfm?uri=ao-31-12-1920

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	Rural Small (M1)				Oceanic (M4)

		r_eff				r_eff

RH	r_j	σ = 0.15	σ = 0.3	σ = 0.4	r_j	σ = 0.15	σ = 0.3	σ = 0.4
0	0.0270	0.036	0.089	0.225	0.160	0.216	0.527	1.283
50	0.0275	0.037	0.091	0.230	0.171	0.231	0.564	1.363
70	0.0285	0.038	0.094	0.238	0.204	0.275	0.673	1.593
80	0.0327	0.044	0.109	0.275	0.318	0.429	1.047	2.284
90	0.0388	0.053	0.129	0.325	0.380	0.512	1.248	2.599
95	0.0424	0.057	0.139	0.350	0.461	0.621	1.507	2.958
98	0.0475	0.064	0.157	0.396	0.602	0.812	1.947	3.473
99	0.0522	0.070	0.172	0.435	0.751	1.011	2.380	3.897
	Rural Large (M3)				Urban Large (M2)

		r_eff				r_eff

RH	r_j	σ = 0.15	σ = 0.3	σ = 0.4	r_j	σ = 0.15	σ = 0.3	σ = 0.4

0	0.430	0.579	1.409	2.828	0.400	0.539	1.313	2.693
50	0.438	0.590	1.435	2.862	0.411	0.554	1.349	2.745
70	0.457	0.616	1.496	2.942	0.478	0.644	1.562	3.028
80	0.548	0.738	1.781	3.289	0.581	0.782	1.879	3.400
90	0.646	0.870	2.078	3.608	0.706	0.951	2.253	3.780
95	0.708	0.954	2.259	3.785	0.863	1.162	2.686	4.163
98	0.973	1.311	2.966	4.386	1.169	1.575	3.419	4.717
99	1.176	1.584	3.433	4.726	1.486	2.002	4.033	5.125
	Biomodal (Maritime)				Stratospheric

r₁	r₂	r_eff			Altitude (km)	r_j	σ_j	r_eff

		σ = 0.15	σ = 0.3	σ = 0.4

0.027	0.160	0.083	0.205	0.502	16.5	0.275	1.408	1.280
0.0275	0.171	0.091	0.224	0.548	17.5	0.258	1.375	0.987
0.0285	0.204	0.119	0.291	0.698	19.5	0.250	1.320	0.694
0.0327	0.318	0.230	0.563	1.233	21.5	0.256	1.233	0.458
0.0388	0.380	0.277	0.677	1.413	23.5	0.235	1.244	0.442
0.0424	0.461	0.366	0.889	1.736	25.5	0.241	1.123	0.288
0.0475	0.602	0.527	1.264	2.212	27.5	0.220	1.082	0.238
0.0522	0.751	0.707	1.660	2.634	29.5	0.211	1.153	0.270

No.	Altitude (km)	Molecular Number Density (m⁻³)	Range of Aerosol Number Density (m⁻³)
1	0	0.243 × 10²⁶	0.1 × 10¹¹ to 0.5 × 10⁸
2	5	0.168 × 10²⁶	0.1 × 10¹¹ to 0.5 × 10⁸
3	10	0.868 × 10²⁵	0.1 × 10¹¹ to 0.2 × 10⁸
4	15	0.477 × 10²⁵	0.3 × 10¹⁰ to 0.5 × 10⁷
5	20	0.196 × 10²⁵	0.3 × 10¹⁰ to 0.2 × 10⁷
6	25	0.831 × 10²⁴	0.3 × 10¹⁰ to 0.2 × 10⁷

	Values of Co for Different Values of ν

ν	2	3	4	5
1.35	−2.9	−3.3	−3.9	−3.8
1.5	−2.5	−2.6	−3.1	−3.3
1.6	−1.7	−1.9	−2.6	−3.2
1.5–0.005i	−3.9	−3.4	−3.5	−3.7
1.5–0.01i	−4.0	−3.7	−3.7	−3.7
1.5–0.05i	−5.8	−5.1	−4.6	−4.3

Aerosol model	r_eff and (RH/ν)	All values of R			R < 10		R ≥ 10

		p	q	−C₀	u	v	u	ν
Rural small (M1)	0.225	0.754	0.993	3.40	2.63	1.050	0.962	0.661
	RH = 0
	0.238	0.749	0.993	3.30	2.71	1.020	0.749	0.510
	RH = 70
	0.325	0.715	0.994	3.20	2.64	0.999	0.476	0.409
	RH = 90
	0.396	0.688	0.995	3.00	2.72	0.957	0.384	0.256
	RH = 98
Oceanic (M4)	1.283	0.479	0.998	2.50	2.23	0.915	0.347	0.214
	RH = 0
	1.593	0.454	1.000	2.50	2.04	0.914	0.310	0.248
	RH = 70
	2.599	0.360	0.959	2.50	1.29	0.733	0.971	0.665
	RH = 90
	3.473	0.296	0.878	2.50	1.02	0.592	1.322	0.665
	RH = 98
Bimodal	0.502	0.632	0.994	2.90	2.65	0.977	0.477	0.348
	RH = 0
	0.698	0.590	0.995	2.80	2.56	0.970	0.427	0.319
	RH = 70
	1.413	0.530	0.995	2.70	2.35	0.961	0.358	0.298
	RH = 90
	2.212	0.502	0.995	2.60	2.28	0.931	0.334	0.241
	RH = 98
Power law	5.030	0.499	1.000	2.50	1.86	0.747	0.324	0.236
	ν = 2
	2.010	0.519	0.996	2.60	2.35	0.914	0.350	0.226
	ν = 3
	0.367	0.689	0.994	3.10	2.65	0.988	0.452	0.376
	ν = 4
	0.149	0.754	0.993	3.30	2.74	1.020	0.818	0.523
	ν = 5
Stratospheric model	0.694	0.765	0.990	2.77	3.54	0.830	3.540	0.830
	h = 20
	0.288	0.856	0.973	2.77	4.33	0.801	4.330	0.801
	h = 25

	Rural Small (M1)				Oceanic (M4)

		r_eff				r_eff

RH	r_j	σ = 0.15	σ = 0.3	σ = 0.4	r_j	σ = 0.15	σ = 0.3	σ = 0.4
0	0.0270	0.036	0.089	0.225	0.160	0.216	0.527	1.283
50	0.0275	0.037	0.091	0.230	0.171	0.231	0.564	1.363
70	0.0285	0.038	0.094	0.238	0.204	0.275	0.673	1.593
80	0.0327	0.044	0.109	0.275	0.318	0.429	1.047	2.284
90	0.0388	0.053	0.129	0.325	0.380	0.512	1.248	2.599
95	0.0424	0.057	0.139	0.350	0.461	0.621	1.507	2.958
98	0.0475	0.064	0.157	0.396	0.602	0.812	1.947	3.473
99	0.0522	0.070	0.172	0.435	0.751	1.011	2.380	3.897
	Rural Large (M3)				Urban Large (M2)

		r_eff				r_eff

RH	r_j	σ = 0.15	σ = 0.3	σ = 0.4	r_j	σ = 0.15	σ = 0.3	σ = 0.4

0	0.430	0.579	1.409	2.828	0.400	0.539	1.313	2.693
50	0.438	0.590	1.435	2.862	0.411	0.554	1.349	2.745
70	0.457	0.616	1.496	2.942	0.478	0.644	1.562	3.028
80	0.548	0.738	1.781	3.289	0.581	0.782	1.879	3.400
90	0.646	0.870	2.078	3.608	0.706	0.951	2.253	3.780
95	0.708	0.954	2.259	3.785	0.863	1.162	2.686	4.163
98	0.973	1.311	2.966	4.386	1.169	1.575	3.419	4.717
99	1.176	1.584	3.433	4.726	1.486	2.002	4.033	5.125
	Biomodal (Maritime)				Stratospheric

r₁	r₂	r_eff			Altitude (km)	r_j	σ_j	r_eff

		σ = 0.15	σ = 0.3	σ = 0.4

0.027	0.160	0.083	0.205	0.502	16.5	0.275	1.408	1.280
0.0275	0.171	0.091	0.224	0.548	17.5	0.258	1.375	0.987
0.0285	0.204	0.119	0.291	0.698	19.5	0.250	1.320	0.694
0.0327	0.318	0.230	0.563	1.233	21.5	0.256	1.233	0.458
0.0388	0.380	0.277	0.677	1.413	23.5	0.235	1.244	0.442
0.0424	0.461	0.366	0.889	1.736	25.5	0.241	1.123	0.288
0.0475	0.602	0.527	1.264	2.212	27.5	0.220	1.082	0.238
0.0522	0.751	0.707	1.660	2.634	29.5	0.211	1.153	0.270

Abstract

Corrections

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Figures (12)

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Equations (12)

Applied Optics