Comparison of various linear depolarization parameters measured by lidar

Francesco Cairo; Guido Di Donfrancesco; Alberto Adriani; Lucio Pulvirenti; Federico Fierli

doi:10.1364/AO.38.004425

Applied Optics
Vol. 38,
Issue 21,
pp. 4425-4432
(1999)
•https://doi.org/10.1364/AO.38.004425

Comparison of various linear depolarization parameters measured by lidar

Francesco Cairo, Guido Di Donfrancesco, Alberto Adriani, Lucio Pulvirenti, and Federico Fierli

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Francesco Cairo, Guido Di Donfrancesco, Alberto Adriani, Lucio Pulvirenti, and Federico Fierli, "Comparison of various linear depolarization parameters measured by lidar," Appl. Opt. 38, 4425-4432 (1999)

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Abstract

Different definitions for estimating the degree of changes in signal polarization measured by lidar measurements are used both to detect the presence of nonspherical aerosol particles and to estimate their shape and density. Our aim is to provide a tool for calculation and interpretation of changes in polarization that are due to aerosol backscatter measured by the lidar technique. An overview of several techniques used to calculate linear depolarization from two-channel lidar measurements is given. Advantages and disadvantages of each method are analyzed when we apply them on a lidar vertical profile. Systematic errors are also discussed. First, an overview of different estimations of polarizability of atmospheric molecules is given. The presence of signal with orthogonal polarization in each channel (cross talk) is a source of error in depolarization estimation. It is calculated at various degrees of contamination, and the total uncertainty on depolarization definition is retrieved.

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Symbol	Definition	Reference
δ	Volume depolarization	6
R ^⊥	Backscatter ratio	7
δ_a	Aerosol depolarization	8
δ_T	Depolarization ratio	9
δ_TA	Aerosol depolarization	10

Parameter	Formula	Calculation Features	Formula f(R, δ, δ_m)
δ	$δ = \frac{β_{a}^{⊥} + β_{m}^{⊥}}{β_{a}^{‖} + β_{m}^{‖}}$	No processing on the raw data
R ^⊥	$R^{⊥} = \frac{β_{m}^{⊥} + β_{a}^{⊥}}{β_{m}^{⊥}}$	β_m needed	$R^{⊥} = \frac{(1 + δ_{m}) δ}{(1 + δ) δ_{m}} R$
D	$D = \frac{R^{⊥}}{R^{‖}}$	β_m needed, unstable where R < 1.1	$D = \frac{δ}{δ_{m}}$
δ_A	$δ_{A} = \frac{β_{a}^{⊥}}{β_{a}^{‖}}$	β_m needed, unstable where R < 1.1	$δ_{A} = \frac{R δ (δ_{m} + 1) - δ_{m} (δ + 1)}{R (δ_{m} + 1) - (δ + 1)}$
δ_T	$δ_{T} = \frac{β_{a}^{⊥} + β_{m}^{⊥}}{β_{a}^{⊥} + β_{m}^{⊥} + β_{a}^{‖} + β_{m}^{‖}}$	No processing on the raw data	$δ_{T} = \frac{δ}{δ + 1}$
δ_TA	$δ_{TA} = \frac{β_{a}^{⊥}}{β_{a}^{⊥} + β_{a}^{‖}}$	β_m needed, unstable where R < 1.1	$δ_{TA} = \frac{R δ (1 + δ_{m}) - δ_{m} (1 + δ)}{(1 + δ) (1 + δ_{m}) (R - 1)}$

Parameter	Tropospheric	Type Ib	I Depol. Layer	II Depol. Layer	Aerosol Free
δ	0.03	0.005	0.14	0.08	0.014
R ^⊥	3	4	100	—	1
D	2	0.4	9–10	5	1
δ_a	0.12	0.005	0.14	0.19	Undefined
δ_T	0.03	0.005	0.13	0.07	0.014
δ_TA	0.11	0.005	0.12	0.17	Undefined

Parameter	Cross-Talk Layer I	Type Ib	Dep. Layer I
δ	1.5	0.33	2
R ^⊥	4	0.5	5
D	1.8	0.6	2
δ_a	3	0.3	3
δ_T	1.6	0.5	2
δ_TA	3	0.3	3

Symbol	Definition	Reference
δ	Volume depolarization	6
R ^⊥	Backscatter ratio	7
δ_a	Aerosol depolarization	8
δ_T	Depolarization ratio	9
δ_TA	Aerosol depolarization	10

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Applied Optics