Mie-Theory Computations of Lidar and Nephelometric Scattering Parameters for Power Law Aerosols

Halstead Harrison; Jack Herbert; Alan P. Waggoner

doi:10.1364/AO.11.002880

Applied Optics
Vol. 11,
Issue 12,
pp. 2880-2885
(1972)
•https://doi.org/10.1364/AO.11.002880

Mie-Theory Computations of Lidar and Nephelometric Scattering Parameters for Power Law Aerosols

Halstead Harrison, Jack Herbert, and Alan P. Waggoner

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Halstead Harrison, Jack Herbert, and Alan P. Waggoner, "Mie-Theory Computations of Lidar and Nephelometric Scattering Parameters for Power Law Aerosols," Appl. Opt. 11, 2880-2885 (1972)

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Abstract

The ratios of lidar backscatter to nephelometric total scattering cross sections have been computed for power law aerosols. Effects were explored of variations of size distributions, indices of refraction, and of radial inhomogeneity of the scattering particles. Reasonable values for these parameters can be chosen so that observed and computed backscatter ratios agree. The general angle-resolved differential scattering problem is discussed briefly with emphasis upon derivable information from scattering measurements in the atmosphere.

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$\begin{array}{r} r_{1} \\ r_{2} \end{array}} μ$	0.04	0.08	0.04	0.08
$\begin{array}{r} r_{1} \\ r_{2} \end{array}} μ$	10.	10.	3.	3.	n′
v = 2.5	0.607	0.603	0.575	0.571	0.0
	0.595	0.592	0.570	0.567	0.0001
	0.540	0.536	0.540	0.536	0.001
	0.369	0.364	0.390	0.384	0.01
	0.249	0.243	0.265	0.257	0.025
	0.136	0.127	0.145	0.135	0.063
	0.108	0.098	0.115	0.104	0.1
	0.103	0.091	0.110	0.096	0.16
	0.142	0.123	0.153	0.132	0.4
	0.292	0.250	0.309	0.262	1.
r = 3.0	0.490	0.478	0.476	0.464	0.0
	0.485	0.474	0.473	0.462	0.0001
	0.395	0.447	0.456	0.434	0.001
	0.352	0.338	0.357	0.343	0.01
	0.266	0.249	0.271	0.253	0.025
	0.184	0.162	0.187	0.165	0.063
	0.166	0.141	0.169	0.143	0.1
	0.168	0.138	0.171	0.141	0.16
	0.234	0.188	0.240	0.192	0.4
	0.431	0.343	0.439	0.349	1.
v = 3.5	0.432	0.404	0.428	0.399	0.0
	0.430	0.402	0.427	0.398	0.0001
	0.418	0.389	0.417	0.388	0.001
	0.357	0.324	0.358	0.325	0.01
	0.303	0.265	0.304	0.266	0.025
	0.253	0.207	0.254	0.208	0.063
	0.247	0.195	0.248	0.196	0.1
	0.260	0.200	0.261	0.201	0.16
	0.353	0.265	0.355	0.267	0.4
	0.581	0.440	0.583	0.442	1.
v = 4.0	0.441	0.381	0.439	0.379	0.0
	0.440	0.380	0.439	0.379	0.0001
	0.434	0.373	0.434	0.373	0.001
	0.402	0.336	0.402	0.336	0.01
	0.372	0.300	0.372	0.300	0.025
	0.350	0.266	0.350	0.266	0.063
	0.354	0.262	0.355	0.262	0.1
	0.376	0.272	0.377	0.272	0.16
	0.488	0.347	0.489	0.348	0.4
	0.725	0.531	0.725	0.531	1.

$\begin{array}{r} r_{1} \\ r_{2} \end{array}} μ$	0.04	0.08	0.04	0.08
$\begin{array}{r} r_{1} \\ r_{2} \end{array}} μ$	10.	10.	3.	3.	n′
v = 2.5	0.674	0.671	0.367	0.362	0.0
	0.432	0.427	0.301	0.304	0.003
	0.236	0.230	0.224	0.216	0.01
	0.119	0.111	0.127	0.119	0.03
	0.077	0.066	0.085	0.073	0.1
	0.085	0.069	0.095	0.077	0.3
v = 3.0	0.393	0.379	0.286	0.270	0.0
	0.300	0.285	0.256	0.240	0.003
	0.217	0.199	0.211	0.193	0.01
	0.158	0.137	0.161	0.140	0.03
	0.140	0.113	0.144	0.116	0.1
	0.168	0.126	0.173	0.131	0.3
v = 3.5	0.310	0.275	0.280	0.243	0.0
	0.280	0.242	0.267	0.229	0.003
	0.249	0.209	0.247	0.207	0.01
	0.225	0.180	0.227	0.182	0.03
	0.228	0.173	0.230	0.174	0.1
	0.281	0.199	0.283	0.201	0.3
v = 4.0	0.348	0.274	0.340	0.266	0.0
	0.339	0.264	0.336	0.260	0.003
	0.329	0.251	0.329	0.251	0.01
	0.325	0.241	0.325	0.241	0.03
	0.344	0.244	0.344	0.244	0.1
	0.416	0.280	0.416	0.281	0.3

$\begin{array}{r} r_{1} \\ r_{2} \end{array}} μ$	0.04	0.08	0.04	0.08
$\begin{array}{r} r_{1} \\ r_{2} \end{array}} μ$	10.	10.	3.	3.	n′
v = 2.5	0.079	0.075	0.072	0.067	1.33
	0.155	0.150	0.133	0.128	1.40
	0.236	0.230	0.224	0.216	1.50
	0.302	0.295	0.273	0.265	1.60
v = 3.0	0.104	0.091	0.102	0.089	1.33
	0.158	0.143	0.150	0.135	1.40
	0.217	0.199	0.211	0.193	1.50
	0.245	0.224	0.234	0.212	1.60
v = 3.5	0.162	0.130	0.163	0.130	1.33
	0.204	0.168	0.202	0.166	1.40
	0.249	0.209	0.227	0.207	1.50
	0.269	0.224	0.266	0.221	1.60
v = 4.0	0.262	0.192	0.262	0.192	1.33
	0.294	0.220	0.294	0.220	1.40
	0.329	0.251	0.329	0.251	1.50
	0.348	0.265	0.347	0.264	1.60

$\begin{array}{r} r_{1} \\ r_{2} \end{array}} μ$	0.04	0.08	0.04	0.08
$\begin{array}{r} r_{1} \\ r_{2} \end{array}} μ$	10.	10.	3.	3.	n′
v = 2.5	0.050	0.046	0.055	0.050	1.33
	0.084	0.078	0.086	0.079	1.40
	0.119	0.111	0.127	0.119	1.50
	0.130	0.120	0.138	0.128	1.60
v = 3.0	0.091	0.077	0.094	0.079	1.33
	0.122	0.105	0.124	0.106	1.40
	0.158	0.137	0.161	0.140	1.50
	0.173	0.149	0.177	0.152	1.60
v = 3.5	0.162	0.126	0.164	0.127	1.33
	0.191	0.151	0.192	0.152	1.40
	0.225	0.180	0.227	0.182	1.50
	0.245	0.195	0.246	0.196	16.0
v = 4.0	0.270	0.194	0.270	0.194	1.33
	0.295	0.215	0.295	0.216	1.4J
	0.325	0.241	0.325	0.241	1.50
	0.344	0.255	0.345	0.256	1.60

$\begin{array}{r} r_{1} \\ r_{2} \end{array}} μ$	0.04	0.08	0.04	0.08
$\begin{array}{r} r_{1} \\ r_{2} \end{array}} μ$	10.	10.	3.	3.	n′
v = 2.5	0.057	0.039	0.052	0.044	1.33
	0.059	0.051	0.065	0.056	1.40
	0.077	0.066	0.085	0.073	1.50
	0.094	0.081	0.102	0.088	1.60
v = 3.0	0.098	0.078	0.102	0.081	1.33
	0.115	0.093	0.120	0.096	1.40
	0.140	0.113	0.144	0.116	1.50
	0.160	0.130	0.165	0.133	1.60
v = 3.5	0.183	0.136	0.185	0.137	1.33
	0.202	0.152	0.204	0.153	1.40
	0.228	0.173	0.230	0.174	1.50
	0.250	0.189	0.251	0.190	1.60
v = 4.0	0.304	0.212	0.305	0.213	1.33
	0.321	0.225	0.322	0.226	1.40
	0.344	0.244	0.344	0.244	1.50
	0.361	0.257	0.362	0.258	1.60

Parameter, ρ	Sensitivity (ρ/A)(∂A/∂ρ)
(n − 1)	+1.0
n′	−0.16
r₁	−0.13
r₂	+0.03
v	+0.44
Fuzz^b	−0.36

Abstract

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Tables (6)

Equations (1)

Applied Optics