Notes on Rayleigh scattering in lidar signals

Mariana Adam

doi:10.1364/AO.51.002135

Applied Optics
Vol. 51,
Issue 12,
pp. 2135-2149
(2012)
•https://doi.org/10.1364/AO.51.002135

Notes on Rayleigh scattering in lidar signals

Mariana Adam

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Mariana Adam, "Notes on Rayleigh scattering in lidar signals," Appl. Opt. 51, 2135-2149 (2012)

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- Atmospheric and Oceanic Optics
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About this Article
History
- Original Manuscript: September 15, 2011
- Revised Manuscript: February 9, 2012
- Manuscript Accepted: February 17, 2012
- Published: April 20, 2012

Abstract

Classical and quantum formulations are used to estimate Rayleigh scattering within lidar signals. Within the classical approach, three scenarios are used to characterize atmospheric molecular composition: 2-component atmosphere ( $N_{2}$ and $O_{2}$ ), 4-component atmosphere ( $N_{2}$ , $O_{2}$ , Ar, and ${CO}_{2}$ ), and 5-component atmosphere ( $N_{2}$ , $O_{2}$ , Ar, ${CO}_{2}$ , and water vapor). First, analysis focuses on Rayleigh scattering, showing the relative difference between the three scenarios within classical approach. The relative difference in molecular scattering between 2(4)-component atmosphere and 5-component atmosphere is below $\sim 1 %$ . The second analysis focuses on the lidar retrieval of aerosol backscatter and extinction coefficients showing the effect of different molecular formulations. A relative difference of $\pm 3 %$ was found between the molecular formulation of 2-component atmosphere and the molecular formulation of 5-component atmosphere. Consideration of the Raman rotational lines blocked by the interference filter is important for the elastic channels, but of little significance in the $N_{2}$ Raman channel. For lidar retrieval of aerosol profiles, the 5-component approximation is the best when the water vapor profile is known, but 2-component is still adequate and quite accurate when water vapor is only poorly known.

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Corrections

Mariana Adam, "Notes on Rayleigh scattering in lidar signals: erratum," Appl. Opt. 62, 3003-3003 (2023)
https://opg.optica.org/ao/abstract.cfm?uri=ao-62-12-3003

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	Temporal Variation				Altitude Variation
	$100 (σ_{m, 2 c} / σ_{m, 5 c} - 1)$ ) (%)		$100 (σ_{m, 4 c} / σ_{m, 5 c} - 1)$ (%)		$100 (σ_{m, 2 c} / σ_{m, 5 c} - 1)$ (%)		$100 (σ_{m, 4 c} / σ_{m, 5 c} - 1)$ (%)
λ [nm]	Mina	Maxb	Mina	Maxb	Minc	Maxd	Minc	Maxd
308	0.3377	0.9421	0.2705	0.8746	0.0670	0.7139	0	0.6465
351	0.3424	0.9687	0.2803	0.9063	0.0619	0.7322	0	0.6699
354.72	0.3427	0.9704	0.2809	0.9082	0.0616	0.7333	0	0.6713
355	0.3425	0.9705	0.2809	0.9084	0.0616	0.7334	0	0.6714
386.69	0.3447	0.9821	0.2852	0.9222	0.0594	0.7414	0	0.6816
400	0.3454	0.9860	0.2866	0.9268	0.0587	0.7441	0	0.6850
407.54	0.3458	0.9880	0.2873	0.9292	0.0583	0.7455	0	0.6868
510.6	0.3504	1.0092	0.2947	0.9531	0.0556	0.7604	0	0.7044
532	0.3512	1.0124	0.2957	0.9566	0.0553	0.7627	0	0.7070
532.075	0.3512	1.0124	0.2957	0.9566	0.0553	0.7627	0	0.7070
607.41	0.3538	1.0220	0.2989	0.9668	0.0547	0.7696	0	0.7145
710	0.3563	1.0312	0.3018	0.9763	0.0544	0.7763	0	0.7215
800	0.3580	1.0368	0.3036	0.9821	0.0542	0.7804	0	0.7258
1064	0.3609	1.0466	0.3066	0.9919	0.0542	0.7876	0	0.7330
1064.15	0.3609	1.0466	0.3066	0.9919	0.0542	0.7876	0	0.7330
1570	0.3639	1.0546	0.3088	0.9991	0.0550	0.7937	0	0.7383
2050	0.3662	1.0587	0.3096	1.0017	0.0564	0.7971	0	0.7402

λ [nm]	$y = a x + b$ a	$y = a x + b$ b
308	$y = 0.0410 x + 0.0727$	$y = 0.0410 x + 0.00576$
351	$y = 0.0425 x + 0.0678$	$y = 0.0425 x + 0.00589$
354.72	$y = 0.0426 x + 0.0675$	$y = 0.0426 x + 0.00590$
355	$y = 0.0426 x + 0.0675$	$y = 0.0426 x + 0.00590$
386.69	$y = 0.0433 x + 0.0653$	$y = 0.0432 x + 0.00595$
400	$y = 0.0435 x + 0.0646$	$y = 0.0435 x + 0.00597$
407.54	$y = 0.0436 x + 0.0643$	$y = 0.0436 x + 0.00598$
510.6	$y = 0.0447 x + 0.0617$	$y = 0.0447 x + 0.00608$
532	$y = 0.0449 x + 0.0614$	$y = 0.0449 x + 0.00609$
532.075	$y = 0.0449 x + 0.0614$	$y = 0.0449 x + 0.00609$
607.41	$y = 0.0454 x + 0.0609$	$y = 0.0453 x + 0.00613$
710	$y = 0.0458 x + 0.0605$	$y = 0.0458 x + 0.00616$
800	$y = 0.0461 x + 0.0604$	$y = 0.0461 x + 0.00619$
1064	$y = 0.0465 x + 0.0604$	$y = 0.0465 x + 0.00622$
1064.15	$y = 0.0465 x + 0.0604$	$y = 0.0465 x + 0.00622$
1570	$y = 0.0469 x + 0.0612$	$y = 0.0469 x + 0.00625$
2050	$y = 0.0470 x + 0.0627$	$y = 0.0470 x + 0.00626$

λ (nm)	2-comp	4-comp	Mina 5-comp	Maxb 5-comp
308	$- 0.063$	$- 0.043$	0.174	0.807
351	$- 0.005$	0.013	0.242	0.911
354.72	$- 0.003$	0.015	0.245	0.916
355	$- 0.002$	0.015	0.245	0.916
386.69	0.010	0.026	0.261	0.948
400	0.012	0.027	0.265	0.957
407.54	0.012	0.028	0.266	0.961
510.6	$- 0.043$	$- 0.028$	0.219	0.940
532	$- 0.056$	$- 0.041$	0.208	0.932
532.075	$- 0.056$	$- 0.041$	0.207	0.932
607.41	$- 0.110$	$- 0.096$	0.156	0.892
710	$- 0.164$	$- 0.150$	0.106	0.851
800	$- 0.196$	$- 0.181$	0.076	0.827
1064	$- 0.248$	$- 0.233$	0.028	0.788
1064.15	$- 0.248$	$- 0.233$	0.028	0.788
1570	$- 0.285$	$- 0.269$	$- 0.006$	0.761
2050	$- 0.298$	$- 0.281$	$- 0.017$	0.753

	Temporal Variation				Altitude Variation
	$100 (σ_{m, 2 c} / σ_{m, 5 c} - 1)$ ) (%)		$100 (σ_{m, 4 c} / σ_{m, 5 c} - 1)$ (%)		$100 (σ_{m, 2 c} / σ_{m, 5 c} - 1)$ (%)		$100 (σ_{m, 4 c} / σ_{m, 5 c} - 1)$ (%)
λ [nm]	Mina	Maxb	Mina	Maxb	Minc	Maxd	Minc	Maxd
308	0.3377	0.9421	0.2705	0.8746	0.0670	0.7139	0	0.6465
351	0.3424	0.9687	0.2803	0.9063	0.0619	0.7322	0	0.6699
354.72	0.3427	0.9704	0.2809	0.9082	0.0616	0.7333	0	0.6713
355	0.3425	0.9705	0.2809	0.9084	0.0616	0.7334	0	0.6714
386.69	0.3447	0.9821	0.2852	0.9222	0.0594	0.7414	0	0.6816
400	0.3454	0.9860	0.2866	0.9268	0.0587	0.7441	0	0.6850
407.54	0.3458	0.9880	0.2873	0.9292	0.0583	0.7455	0	0.6868
510.6	0.3504	1.0092	0.2947	0.9531	0.0556	0.7604	0	0.7044
532	0.3512	1.0124	0.2957	0.9566	0.0553	0.7627	0	0.7070
532.075	0.3512	1.0124	0.2957	0.9566	0.0553	0.7627	0	0.7070
607.41	0.3538	1.0220	0.2989	0.9668	0.0547	0.7696	0	0.7145
710	0.3563	1.0312	0.3018	0.9763	0.0544	0.7763	0	0.7215
800	0.3580	1.0368	0.3036	0.9821	0.0542	0.7804	0	0.7258
1064	0.3609	1.0466	0.3066	0.9919	0.0542	0.7876	0	0.7330
1064.15	0.3609	1.0466	0.3066	0.9919	0.0542	0.7876	0	0.7330
1570	0.3639	1.0546	0.3088	0.9991	0.0550	0.7937	0	0.7383
2050	0.3662	1.0587	0.3096	1.0017	0.0564	0.7971	0	0.7402

λ [nm]	$y = a x + b$ a	$y = a x + b$ b
308	$y = 0.0410 x + 0.0727$	$y = 0.0410 x + 0.00576$
351	$y = 0.0425 x + 0.0678$	$y = 0.0425 x + 0.00589$
354.72	$y = 0.0426 x + 0.0675$	$y = 0.0426 x + 0.00590$
355	$y = 0.0426 x + 0.0675$	$y = 0.0426 x + 0.00590$
386.69	$y = 0.0433 x + 0.0653$	$y = 0.0432 x + 0.00595$
400	$y = 0.0435 x + 0.0646$	$y = 0.0435 x + 0.00597$
407.54	$y = 0.0436 x + 0.0643$	$y = 0.0436 x + 0.00598$
510.6	$y = 0.0447 x + 0.0617$	$y = 0.0447 x + 0.00608$
532	$y = 0.0449 x + 0.0614$	$y = 0.0449 x + 0.00609$
532.075	$y = 0.0449 x + 0.0614$	$y = 0.0449 x + 0.00609$
607.41	$y = 0.0454 x + 0.0609$	$y = 0.0453 x + 0.00613$
710	$y = 0.0458 x + 0.0605$	$y = 0.0458 x + 0.00616$
800	$y = 0.0461 x + 0.0604$	$y = 0.0461 x + 0.00619$
1064	$y = 0.0465 x + 0.0604$	$y = 0.0465 x + 0.00622$
1064.15	$y = 0.0465 x + 0.0604$	$y = 0.0465 x + 0.00622$
1570	$y = 0.0469 x + 0.0612$	$y = 0.0469 x + 0.00625$
2050	$y = 0.0470 x + 0.0627$	$y = 0.0470 x + 0.00626$

Abstract

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Tables (3)

Equations (29)

Applied Optics