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Polarization lidar returns from aerosolsand thin clouds: a framework for the analysis

Gian Paolo Gobbi

Relationships for the interpretation of polarization lidar observations of aerosols and thin clouds arepresented. They allow for the separation of contributions to backscatter from solid and liquid phases bythe use of either the classical backscatter and depolarization ratio parameters or the particulate cross-polarized backscatter cross sections. It is shown that different aerosol phases can be better separatedby use of the latter coordinates. Emphasis is placed on the study of composition and phase propertiesof polar stratospheric aerosols. © 1998 Optical Society of America

OCIS codes: 010.1100, 010.3640, 010.1280.

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1. Introduction

Lidars ~laser radars! are excellent detectors of opti-cally thin clouds.1 Lasers usually employed for this

urpose generate short pulses of polarized light.herefore, radiation backscattered by homogeneouspherical particles will maintain the original ~paral-el! polarization, whereas nonspherical particles willnduce some degree of depolarization. This depolar-zation is measured by the depolarization ratio D 5

S'yS" between the returned cross-polarized signalS' and the parallel-polarized signal S". In the ab-sence of aerosols or particles ~Rayleigh scattering!,anisotropy in the structure of air molecules generatesa small amount of depolarization Dm, typically of therder of 1.4%.2 In the case of scattering by particles,

the degree of depolarization depends on a large num-ber of variables such as size and shape distributions,refractive index, and phase.3,4 The number of suchunknowns is usually much larger than the number ofmeasured parameters. One has to make some as-sumptions about particle characteristics to managethe lidar inversion problem. Depending on the num-ber of these assumptions, the interpretation of depo-larization observations can become quite qualitative.Nevertheless, polarization lidars have been exten-sively employed when assessment of particle phasewas of some importance. For example, lidar studies

The author is with the Istituto di Fisica dell’Atmosfera, ConsiglioNazionale delle Ricerche, Via Fosso del Cavaliere, 00133 Rome,Italy.

Received 24 March 19980003-6935y98y245505-04$15.00y0© 1998 Optical Society of America

of clouds have shown that ice crystals induceamounts of depolarization that vary approximatelybetween 40% and 70%.5 Special cases such as ori-ented crystals and complex crystals have also beenreported to induce null depolarization and D $ 100%,respectively. However, accurate laboratory andfield studies have shown that simple ice crystals gen-erate a surprisingly constant amount of depolariza-tion Dc of the order of 50%, which can be decreasedmainly by the presence of liquid particles, i.e., inmixed phases.5–7 Hereafter the symbol Dc will indi-cate the depolarization ratio of crystals alone, as op-posed to the total ~i.e., that which is due to moleculesplus spherical and nonspherical particles! lidar depo-arization ratio D. Further below, it is demon-trated that Dc represents the maximum value that D

can reach. A second interesting result from the lit-erature is one that shows that depolarization Dc '50% is also observed in just-frozen spherical waterdroplets, an effect explained by the formation of in-homogeneities in the droplet itself.8

Stratospheric aerosols condense mainly as super-cooled liquid-sulfate droplets, which present a sizeand composition variability smaller than do tropo-spheric particles.9 This behavior allows for polar-ization lidars to better detect changes of phase thatare taking place in the polar stratosphere when nitricacid and water condense to form polar stratosphericclouds ~PSC’s!.10 The study of PSC’s has attractedmuch attention during the past decade or so, as PSC’sprime the Antarctic stratosphere for the developmentof springtime ozone depletion.10 Recent studiesshowed that these clouds are composed of a variety ofparticles that originate from the condensation of am-bient H2SO4, HNO3, and H2O into liquid and solid

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solutions and into crystalline forms. As in thesimple crystals case, PSC’s show maximum depolar-ization ratios of the order of 50%.13–15 In this re-spect, it has been shown that polarization lidarobservations can provide quantitative informationabout solid and liquid composition of the investigatedclouds.15 This paper will complement the latter re-ults by providing relationships useful in the analysisf polarization lidar returns from PSC, aerosols, andptically thin clouds, which are assumed to be anxternal mixture of solid and liquid particles withelative abundances that can vary from 0 to 100%.nalysis of the backscatter cross sections for the two

idar polarizations is used to provide informationbout both the relative weights and the physicalroperties of the observed phases.

2. Backscatter and Depolarization Ratios

Common products of the analysis of polarization lidarreturns are the parallel backscatter ratio,

R 5 ~bm"x1 ba"!ybm", (1)

and the depolarization ratio,

D 5 S'yS" 5 ~bm' 1 ba'!y~bm" 1 ba"!, (2)

where bm and ba represent the molecular and aerosolbackscatter cross sections, respectively. Values ofbm are computed either from radio soundings or fromatmospheric models. Aerosol backscatter cross sec-tions ba' and ba" can then be directly obtained fromhe analysis of the two cross-polarized lidar traces.

particle-free atmosphere is characterized by R 5 1and, as previously indicated, D ' 1.4%. In the caseof stratospheric aerosols, the total backscatter crosssection ba 5 ba' 1 ba" has been shown to be linkedy functional relationships to the particles’ total sur-ace area, volume, and extinction cross section.16

Atmospheric aerosols and cloud particles can be ineither the solid or the liquid phase. In the lattercase the droplets will remain spherical up to sizes ofat least 100 mm.17 The particulate total backscattercross section can then be expressed as

ba 5 bs 1 bc 5 bs 1 bc' 1 bc" , (3)

where s and c represent spherical and crystalline–solid contributions, respectively. This analysis as-sumes that the depolarization induced by solidparticles is constant, an assumption found to hold forPSC, where Dc ' 50%.15 In Section 3 it is shownthat employing lidar perpendicular cross-section co-ordinates clearly indicates the presence of typical de-polarization levels in the observed aerosols. Suchanalysis also allows for separation of solids with dif-ferent Dc values, because these different classes ofparticle are usually related to different temperaturesand altitudes.

The assumption that Dc 5 k leads to

Dc 5 bc'ybc" 5 k. (4)

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By employing Eq. ~3! we obtain

bc' 5 bc 3 ky~1 1 k!, (5)

where ky~1 1 k! represents the fraction of impinginglight depolarized onto the ' plane by the nonspheri-cal particle. For k 5 0.5 we obtain that the amountof depolarized radiation detected at the ' channel isone third of the impinging radiation. Using thisframework, we can rewrite the backscatter and de-polarization ratios as

R 5 ~bm" 1 bs 1 bc"!ybm", (6)

D 5 ~bc' 1 0.014 3 bm"!y~bm" 1 bs 1 bc"!5 @~k 3 bc"ybm"! 1 0.014#yR

5 $0.014 1 k 3 @R 2 1 2 ~bsybm"!#%yR. (7)

Equation ~7! describes two interesting properties ofhe depolarization ratio D: ~1! In the presence ofiquid particles alone ~bc" 5 bc' 5 0! we obtain D 5

0.014yR, i.e., the lidar depolarization ratio can de-crease below D 5 1.4% for increasing values of R and~2! in the absence of liquid particles ~bs 5 0! depolar-ization tends to D 5 0.014 for R tending to 1 andtends to the asymptotic value D 5 k for large valuesof R, reflecting the changing relative weights of bmand ba. Such behavior makes the depolarization ra-tio a quite nonlinear function of R. More generally,D versus R coordinates represent a difficult frame-work for analysis of the depolarization properties ofparticles characterized by bc ' bs 1 bm", i.e., one ofthe most common cases in PSC observations.15

Equation ~7! also indicates how correlation of the tworaces R and D along a vertical interval Dz will be

positive or negative, depending on whether solid orliquid particles dominate the backscatter, a behaviorcommonly observed in PSC profiles.15 In this re-spect, evaluation of the linear correlation coefficientover the height interval Dz can provide qualitativenformation about the phase-dominating backscattern that region.

Further relationships that exploit backscatter andepolarization ratio information are those that relateo one another the backscatter cross sections of thehree atmospheric components addressed above:m, bs, and bc. Considering that the aerosol total

cross section ba 5 bs 1 bc is closely related to thescatterer’s volume, surface area, and extinction crosssection,16 bc and bs can provide first guesses aboutthe relative contributions to these quantities of therelevant phases in the observed cloud. The ratiobetween the backscatter cross sections of sphericalparticles and molecules can be obtained from Eq. ~7!:

bsybm" 5 R 2 1 2 ~R 3 D 2 0.014!yk. (8)

ubstituting bc" 5 bcy~1 1 k! into Eq. ~6! yields theequivalent ratio for solid particles:

bcybm" 5 @~1 1 k!yk#~R 3 D 2 0.014!. (9)

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Finally, we obtain the relative contribution of spheresand solids to backscatter from aerosols by ratioingEqs. ~8! and ~9!:

bsybc 5 @1y~1 1 k!#@k~R 2 1!y~R 3 D 2 0.014! 2 1#.

(10)

Care should be taken in employing these relation-ships when the R 3 D product is close to 0.014 orwhen R ' 1, because errors might grow large. How-ever, both PSC and cirrus clouds present quite high Rand D ratios; therefore Eq. ~10! can be used as a firstguess for determining relative contributions to vol-umes and, possibly, surface areas and extinctions inmixed-phase thin clouds.

3. Perpendicular Cross-Section Coordinates

The relationships defined so far were based on thelidar backscatter ratio R and the depolarization ratioD commonly found in the literature. Another itemof first-level information on particulate scattering ob-tainable from the two cross-polarized lidar signals isrepresented by the backscatter cross sections ba' 5bc' for the perpendicular channel and ba" 5 bs 1 bc"for the parallel channel. These quantities are deter-mined with the same error as R from first inversion ofthe lidar cross-polarized signals. It was shown pre-viously that D is a quite nonlinear function of R. Inthis respect, rather than analyzing observations in Rversus D coordinates it might be convenient to ana-lyze data in bc' versus ba" coordinates, i.e., perpen-dicular cross-section coordinates ~PCC!.15 Thisframework has been shown to provide a direct view ofwhether the data set is characterized by solid parti-cles with a constant Dc value, by liquid particlesalone, or by mixed phases. In fact, in the case ofscattering from crystalline–solid particles ~bs 5 0!characterized by a depolarization ratio Dc 5 k thedata points cluster along a line of constant slope k.

onversely, when all particles are liquid ~bc 5 0!,ata points cluster along the x axis only. Finally,

mixed-phase data points place themselves betweenthese two lines. We can formulate these propertiesby employing Eqs. ~4! and ~5! and by defining as a 5bcybs the ratio between solid and liquid cross sec-tions. We then obtain bs 1 bc" 5 ~bcya! 1 @bcy~k 11!# and, by means of Eq. ~5!,

bc' 5 @~a 3 k!y~1 1 k 1 a!# 3 ~bs 1 bc"!5 C 3 ~bs 1 bc"!. (11)

Equation ~11! provides values of bc' as a function ofthe angular coefficient C and of ~bs 1 bc"!. For bc 50, a 5 0 and C 5 0. For bs 5 0, a 5 ` and theoefficient is C 5 k. For intermediate values of a

~uncorrelated behavior of bs and bc!, bc' will be lo-cated between the C 5 k slope and the x axis. In thease of a constant ratio bcybs, bc' will increase lin-

early with ~bs 1 bc"! along a slope C , k. We candetermine the liquid and solid contributions to back-

scatter for any point in the PCC plot from its coordi-nates by employing Eq. ~4!:

bs 5 ~bs 1 bc"! 2 ~bc'yk!, (12a)

bc 5 bc' 3 ~1 1 k!yk. (12b)

Equations ~12! show how we can separate the contri-bution of liquid phases to backscatter ~bs! from thecontribution from solids ~bc! just by determining thek value that is typical of the investigated cloud, i.e.,the slope of the line that best fits the pure solid–crystalline region of the plotted data. As previouslyintroduced, parameters such as particle volume, sur-face area, and extinction can be inferred from thesebackscatter cross sections.16

Application of this method to the analysis of Ant-arctic polar stratospheric cloud observations15 hasconfirmed that PSC solid particles show quite a con-stant depolarization ratio Dc 5 50% and that several

SC phases and compositions can be identified in theCC plot. To illustrate the potential of the PCC,ig. 1 shows boundaries for various phases and com-ositions of stratospheric aerosols and PSC’s with k 5

Fig. 1. Schematic of backscatter cross-sectional boundaries ~thin-line polygons with labels! for various phases and compositions ofpolar stratospheric aerosols in PCC coordinates as obtained byGobbi et al.15 The presence of solid, depolarizing particles is re-vealed by the increase of bc' above liquid-sulfate background val-

es. The growth of liquid supercooled ternary solutions ~STS!eads to increased bs values to approximately 1 order of magnitude

along the bs 1 bc" axis. Mixed-phase PSC’s containing STS andNO3-based solids as nitric acid trihydrate ~NAT! and metastable

olid phases ~MSP! extend from the STS region along the bc' axis.ll pure solid phases ~from sulfates to ice! grow along a quasi-onstant 50% slope to the top left of the mixed phases. Full nu-leation of aerosols into ice crystals leads to the largest crossections along the 50% slope. In mixed phases containing ice theiquid component departs from the 50% slope by typical STS cross-ectional values. Two 50% slopes ~thick solid curves!, one cross-

ing the x axis at bs 1 bc" 5 0 and the second at bs 1 bc" 5 6 3 1029

~maximum cross section reached by STS! bracket the region ofrowth of polar stratospheric aerosols.

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pretation of cloud radar signals at 94 GHz: an error analysis,”

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1

5

0.5, as obtained by Gobbi et al. These regions arelocated between two 50% slopes, which at bc' 5 0riginate, respectively, at bs 1 bc" 5 0 and at bs 1 bc"

5 6 3 1029 cm21 sr21, the latter being the maximumvalue that liquid supercooled ternary solutions of ni-tric acid, sulfuric acid, and water have shown to reachin that analysis. Stratospheric liquid, solid, andmixed phases composed of sulfates, nitric acid trihy-drate, metastable solid phases, and ice10–12 wereshown to be well separated in these coordinates, withsome overlapping just at the boundaries. In thisrespect, PCC provide a kind of phase diagram that isdirectly derivable from lidar-observed parameters.

In conclusion, relationships that are useful for theinterpretation of polarization lidar observations ofaerosols and thin clouds have been presented.These relationships permit separation of solid andliquid phase contributions to the backscatter of thinclouds by use of either the classic backscatter anddepolarization ratio parameters ~R and D! or the par-ticulate cross-polarized backscatter cross sections bc'

and bs 1 bc". In the latter case it has been shownthat different aerosol phases are easier to visualize insuch coordinates rather than in D-versus-R coordi-nates. In particular, it has been shown that one canidentify and analyze many types of polar strato-spheric cloud and sulfate aerosol by the formulasprovided and by plotting data in the cross-polarizedbackscatter cross-sectional coordinates. Applicationof the method to other kinds of optically thin cloud,e.g., cirrus clouds, strata, and hazes, will provide auseful tool for the study of cloud particle phases bymeans of polarization lidars.

This study was partly funded by the Italian SpaceAgency.

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