parameterization of stratospheric aerosol physical properties on the basis of nd:yag lidar...

Parameterization of stratospheric aerosol physicalproperties on the basis of Nd:YAG lidar observations

Gian Paolo Gobbi

An extension to the 355- and 1064-nm wavelengths of a numerical optical model originally developed at532 nm is presented. The resulting parameterization allows estimates of stratospheric aerosol surfacearea, volume, and extinction-to-backscatter ratio from lidar measurements obtained at one of the twoNd:YAG laser wavelengths. Functional relationships that link single-wavelength backscatter to each ofthe physical variables are provided for sulfate aerosol types ranging from background to heavy volcanicunder environmental conditions representative of the global lower stratosphere. The behavior of thefunctional relationships at the three Nd:YAG wavelengths is compared. Relative errors of model esti-mates range between 10% and 50%, depending on wavelength and backscatter cross sections. Thesevalues are comparable with the ones that characterize in situ particle counters. The inference of particleeffective radius and the application of the method to the interpretation of supercooled polar stratosphericcloud observations are discussed. © 1998 Optical Society of America

OCIS codes: 010.0010, 140.3530, 280.3640, 010.1110.

1. Introduction

Stratospheric aerosols modulate both the global tem-perature and the ozone layer’s chemistry by means ofprocesses such as extinction of solar radiation, acti-vation of heterogeneous chemistry, and sedimenta-tion.1,2 Maximum effects on temperature arenoticed after large volcanic eruptions and, owing tolong residence times, can last for several years.1 Ex-tremely low temperatures reached in the winter polarregions allow condensation of ambient nitric acid andwater onto background sulfate aerosol, leading to theformation of polar stratospheric clouds ~PSC’s!.Thanks to their large surface area and settling speed,PSC’s set up the conditions for the springtime ozonedepletion by both activating ozone-destroying halo-gens and sedimenting halogen-capturing nitrates.2Increasing the total aerosol surface area, volcaniceruptions enhance both photodissociation and theheterogeneous activation of ozone-depleting species,two processes that result in a global, long-lastingozone-reducing action.3 These processes stronglydepend on the aerosol surface area.

The author is with the Consiglio Nazionale delle Ricerche,Istituto di Fisica dell’Atmosfera, Via Fosso del Cavaliere, Rome00133, Italy.

Received 2 September 1997; revised manuscript received 2March 1998.

0003-6935y98y214712-09$15.00y0© 1998 Optical Society of America

4712 APPLIED OPTICS y Vol. 37, No. 21 y 20 July 1998

The stratospheric background aerosol layer peaksat approximately 70 hPa and is formed by dilutedsulfuric acid droplets, which remain supercooled, i.e.,spherical, to as low as at least 192–196 K.4–6 Thedroplets’7 dilution can be determined on the basis ofatmospheric temperature and water content. Un-der typical mid-latitude conditions the stratosphericaerosol is composed of 70% sulfuric acid by weight,whereas in the colder high-latitude stratosphere itdeliquesces to approximately 50% sulfuric acid.7–9

Below approximately 192 K, ambient nitric acidstarts condensing onto sulfate aerosol to form super-cooled ternary solution ~STS! PSC’s, which can re-main liquid to as low as the ice frost-pointtemperature.10 STS’s, which represent the mostcommon type of PSC in the Arctic, are even moreeffective than frozen PSC’s are at activating ozone-depleting species. The assumption of sphericityholds then for all these liquid aerosols, whose scat-tering properties can be computed by means of theMie theory.

Presented here is an extension of the Nd:YAG laserfundamental and triplicated wavelengths ~1064 and355 nm, respectively! of the model developed to esti-mate aerosol physical properties from lidar returns at532 nm.11 On the basis of that model, functionalrelationships linking single-wavelength ~at either355 or 1064 nm! lidar backscatter to aerosol surfacearea, volume, and extinction-to-backscatter ratio areobtained by the study of the average behavior of alarge statistical set of size distributions and compo-

sitions, representative of aerosol ranging from back-ground to postvolcanic sulfates and to STS PSC’s. Anew variable, the aerosol effective radius reff, is alsodiscussed. Sections 2 and 3 provide an overview ofthe approach. For a more complete description seeGobbi.11

2. Aerosol Physical and Optical Properties

The atmospheric backscatter of lidar pulses is gener-ated by the combined contribution of molecular bmand aerosol ba backscatter cross sections per unitvolume.12 In lidar analysis the scattering ratio R 5~ba 1 bm!ybm is commonly employed to represent theaerosol share in the total backscatter, R 5 1 indicat-ing an aerosol-free atmosphere. At 532 nm thebackground aerosol layer shows typical values of R 51.06, whereas maximum post-Pinatubo observationsat 25 km reported R . 100 in the tropics13 and R .10 at mid-latitude.14 In the case of PSC’s, STS’sreach scattering ratios as high as R 5 4–5, and iceones can reach values of the order of R 5 100.15

Typical 532-nm, mid-latitude molecular backscattercross sections at 15, 18, and 25 km are of the order of2.5 3 1029, 1.6 3 1029, and 5.3 3 10210 cm21 sr21,respectively. These values indicate how back-ground aerosol cross sections span the region 10211–10210 cm21 sr21, whereas volcanic aerosol and STSPSC’s grow in the region ba 5 1029–1028 cm21 sr21

and heavy volcanic and ice PSC’s reach in excess of ba5 1028 cm21 sr21.

At the wavelength l the backscatter efficiencyQbs~r, l, m! and the extinction efficiency Qext~r, l, m!of homogeneous, spherical particles of radius r andcomplex refractive index m 5 mre 2 imim can becomputed by means of the Mie theory. The aerosolbackscatter cross section ba is then given by

ba 5 *0

`

Qbs~r, l, m!n~r!pr2dr, (1)

where n~r! is the particle size distribution per unit airvolume. Similarly, one can obtain the extinctioncross section sa by replacing Qbs with Qext in Eq. ~1!.Knowledge of the aerosol extinction-to-backscatterratio Reb 5 sayba is essential to the correction forextinction in the inversion of lidar profiles and to thecomparison of lidar and satellite extinction observa-tions. This ratio is commonly taken as fixed or dis-cretized but hardly ever expressed as a functionalrelationship.

Several curves have been employed to fit the ob-served size distribution of stratospheric aerosol:gamma, log normal, power law, etc.16 The log nor-mal employed here is widely used because it repro-duces well the bell-shaped dispersion ~in log–logcoordinates! of observed aerosol distributions17:

n~r! 5dndr

5N0

rÎ2p ln sg

expF2ln2 ~ryrg!

2 ln2 ~sg!G, (2)

where N0 is the total number of particles per unitvolume and rg and sg are the distribution geometric

radius and width, respectively. Pinnick et al.18 ob-served that the 1971–1973 background aerosol dis-tribution at 18–20 km was fitted well by amonomodal log normal with parameters N0 5 10cm23, rg 5 0.0725 mm, and sg 5 1.86. Volcanicinjections change such status both by condensationof newly formed sulfuric acid on pre-existing aerosoland by homogeneous nucleation of new particles.During these events the Kelvin effect, coagulation,and mixing often lead to the buildup of bimodal dis-tributions, showing a second mode in the micrometer-sized range. Evidence of bimodality is commonlyreported after major volcanic eruptions17,19–21 andmust be taken into account when aerosol optical prop-erties are addressed.11

Finally, a frequently used way to provide typicalaerosol scattering size is the area-weighed distribu-tion effective radius reff

9:

reff 5 F*0

`

n~r!rpr2drGYF*0

`

n~r!pr2drG. (3)

Equation ~3! shows how the effective radius is pro-portional to the ratio between aerosol volume andsurface area in the following way: reff 5 3 VaySa.Furthermore, employing for n~r! the log normal sizedistribution of Eq. ~2! can show that reff 5 rg exp~5y2ln2 sg!. Links between the distribution effective ra-dius and ba are discussed in Subsection 4.D.

3. Aerosol Scattering Model

The purpose here is to provide relationships betweenba at 355 or 1064 nm and aerosol parameters such astotal surface area Sa, volume Va, extinction cross sec-tion sa, extinction-to-backscatter ratio Reb 5 sayba,and effective radius reff. As done for the 532-nmcase,11 this aim is pursued by means of a statisticalapproach, i.e., evaluation of such relationships bymeans of the Mie theory for a large number of aerosolsize distributions, representative of conditions rang-ing from background to postvolcanic. Functionallinks between these variables are then defined on thebasis of the average values of the computed relation-ships. Since observations of real size distributionsare limited in both number and locations, the prob-lem is approached by use of a Monte Carlo technique,i.e., generation of random distributions and composi-tions whose parameters are constrained within ex-perimentally observed boundaries. On the basis ofthe previous discussion distributions are chosen to bemonomodal and bimodal log normals. With the firstand second mode denoted by subscripts 1 and 2, re-spectively, six parameters ~N1, r1, s1, N2, r2, and s2!plus the real mre and the imaginary mim refractiveindices are then needed to define each distributionoptical property. Boundaries to the variability ofeach one of these parameters have been establishedon the basis of a large set of observations reported inthe literature and described in Gobbi.11 These ob-servations cover the physical and chemical variabil-ity of size distributions observed in the global lower

20 July 1998 y Vol. 37, No. 21 y APPLIED OPTICS 4713

Table 1. Boundaries ~Min–Max! to the Random Variability of Distribution Parameters Employed in the Simulationsa

Run N1 ~cm23! r1 ~cm! s1 N2 ~cm23! r2 ~cm! s2 mre mim

355 1.0–30 2.0 3 1026 to 4.0 3 1025 1.3–2.3 1.0 3 1024 to 4 1.5 3 1025 to 3 3 1024 1.1–1.8 1.440–1.480 0.0–1026

532 1.0–30 2.0 3 1026 to 4.0 3 1025 1.3–2.3 1.0 3 1024 to 4 1.5 3 1025 to 3 3 1024 1.1–1.8 1.420–1.460 0.0–1026

1064 1.0–30 2.0 3 1026 to 4.0 3 1025 1.3–2.3 1.0 3 1024 to 4 1.5 3 1025 to 3 3 1024 1.1–1.8 1.405–1.445 0.0–1026

a Note that only refractive-index boundaries change with wavelength.

stratosphere in both background and volcanicallyperturbed conditions. Each synthetic size distribu-tion is then defined by the random generation of theeight parameters within the relevant boundaries.Parameters whose observed variability spans overone decade are randomly generated, with equal prob-ability attributed to each decade. Acceptance of ran-dom parameters is also conditioned by selection rulesderived from the literature. These rules are the fol-lowing11: ~1! N1 . 7.5 N2, ~2! r2 . r1, ~3! r2yr1 # 20,~4! s1 . s2, ~5! s1 , 2 when r1 . 0.1 mm, ~6! s2 , 1.3when r2 . 0.7 mm. For each synthetic distributiongenerated, ba, sa, Sa, Va, and reff are integrated overthe radii range 0.001–25 mm. To be accepted, con-vergence of the integral must be better than1y50,000. Overall, 10,000 synthetic distributions,i.e., 2000 more than in Gobbi,11 are generated to com-plete a case study. The same size distribution andthe same relative change in refractive index are an-alyzed at each wavelength. The average behavior ofthe scatter plots linking ba and the investigated pa-rameter is then computed at 40 logarithmicallyspaced points. Therefore each average point in thefollowing figures is representative, on average, of 250random size distributions. However, single pointsmust represent at least 100 size distributions to beconsidered. A x2 test showed that overall conver-gence of model averages is already better than 99%when as few as 2500 synthetic distributions are em-ployed.

With respect to the variety of simulations carriedout in Ref. 11, employed here is the set of boundarieslabeled in Ref. 11 as run number 99 and reportedhere in Table 1. These boundaries provide the bestmodel for sulfate aerosol ~ranging from background toheavy volcanic! and also for liquid PSC’s. In thatcase the real part of the refractive index was assumedto vary in the range 1.43 # mre # 1.45. Recentresults presented by Russell et al.9 and by Yue et al.8showed that the global-scale variability of the sulfateaerosol refractive index at 532 nm is better describedby a slightly wider range: 1.42 # mre # 1.46. The532-nm reference simulation presented here hasthen been run employing these new boundaries.Refractive-index variability for the 355- and 1064-nmcases has also been obtained from Russell et al.9The complete set of boundaries to the distributionparameters employed here is summarized in Table 1.Simulations are numbered according to the relevantwavelength, with run 532 representing the reference532-nm one, i.e., run 99 in Gobbi.11


4. Model Results

A. Aerosol Surface Area

Average values and relative errors for the relation-ship Sa versus ba at the three wavelengths are pre-sented in Figs. 1~a! and 1~b!, respectively. In thisand the following cases average values are computedat eight equally spaced bins per decade. Every av-erage point is represented by one plotted symbol.Backscatter cross sections ba that were obtained inthe run-532 range between 2 3 10212 and 2 3 1028

cm21 sr21, spanned 4 orders of magnitude. Thelargest cross section that aerosols achieve withinthese boundaries can therefore account for a scatter-ing ratio R $ 10 upward of 15-km altitude and R ' 40at 25 km. The relevant range for Sa is 1.5 3 1029 to8 3 1027 cm2 cm23 ~0.15–80 mm2 cm23!, spanningalmost 3 orders of magnitude. Similarly to whatwas found at 532 nm by Gobbi,11 logarithmic-coordinates relationship Sa versus ba at either 355 or1064 nm is closely approximated by a second-orderpolynomial ~parabolic! curve of the kind

Y 5 a0Y 1 a1YX 1 a2YX2, (4)

where X 5 log ba and Y is the logarithm of the pa-rameter investigated, which in this case is Sa. Thecorresponding equation to evaluate Sa is then

Sa 5 10~a0S 1 a1S X 1 a2S X2!. (5)

The computed least-squares parabolic fits to the runs’average values and their relevant parameters a0S,a1S, and a2S are reported in Fig. 1~a! as solid curvesand in Table 2, respectively. The backscatter cross-section range over which the fit is computed and thecorrelation coefficient, representing the quality of theparabolic approximation, are also reported in Table 2.

Dispersion of results about their average value pro-vides a further characterization of simulations. Rel-ative errors dSaySa ~dSa 5 1s dispersion of computedsurface area values! versus ba for the three casespresented in Fig. 1~a! are plotted in Fig. 1~b!. Theseplots are representative of the accuracy of the modelat estimating Sa. Observational errors ~dbayba! arealso to be considered when the overall quality of theestimate is evaluated. These errors increase for de-creasing values of ba, i.e., when passing from per-turbed to background aerosol conditions. To providean idea of the influence of aerosol backscatter inde-termination on the error in retrieving Sa, Fig. 1~b!also reports typical observational errors as derivedfrom the NASA Langley three-wavelength lidar.22

Figure 1~b! shows how, under background aerosol

conditions, the system-induced error can be of thesame order or even larger than that of the modelestimate, whereas it becomes negligible as soon asperturbed conditions are reached. As observationalerrors also depend on the integration time and sys-tem characteristics, the following discussion neces-sarily addresses model-related errors only.

In the region of background aerosol ~10211–10210

cm21 sr21 at 532 nm! model errors range between40% and 50% and descend below 40% under volcanicor PSC conditions, where smaller errors are attained

Fig. 1. ~a! Average value points of the relationship Sa versus ba

computed at 355 ~open triangles!, 532 ~crossed circles!, and 1064nm ~open squares!. Solid curves show the log–log, second-orderpolynomial fit to the relevant points. Fit parameters are reportedin Table 2. ~b! Solid curves with symbols show relative errorsdSaySa ~dSa 5 1s! of model estimates represented by the fits of ~a!.Single symbols depict typical observational errors at 355 ~filledtriangles!, 532 ~filled circles!, and 1064 nm ~filled squares!, asderived for the NASA Langley three-wavelength lidar.

at shorter wavelengths. Under heavy volcanic andice PSC conditions, dSaySa reaches values as low as10–15% at both 355 and 532 nm ~25% at 1064 nm!.For a given aerosol surface Sa, ba and dSaySa valuesrespectively decrease and increase with wavelength.Therefore surface area estimates are affected bysmaller errors when obtained at shorter wave-lengths. Also, decreasing of Sa estimate errors withincreasing cross sections differs from the opticalcounters’ behavior, whose errors increase with thelowering in the number concentrations, i.e., for largerparticles.23 In evaluating the Mt. Pinatubo aerosolsurface area, Deshler et al.17 reported optical-counteraverage errors to range between 10% and 20%, withmaxima of 60%. In this respect model errors of Saestimates made at each of the three Nd:YAG laserwavelengths compare quite well with the ones char-acterizing these in situ particle-counter observations.

B. Aerosol Volume

Average points of the relationship Va versus ba andthe relevant error dVayVa versus ba are plotted inFigs. 2~a! and 2~b!, respectively. In Fig. 2~b! are alsoreported errors induced by typical lidar signal vari-ability as estimated for the NASA Langley system.22

All points in Fig. 2~a! are approximated well by thesecond-order polynomial fits of Eq. ~4! ~solid curves!,whose parameters are reported in Table 2. Cross-section boundaries over which these fits apply are thesame as in the surface area cases. Similarly to back-scatter cross sections, the particle volume spans 4orders of magnitude. The 532-nm curve showsbackground aerosol to be bracketed by the typicalsulfate volume of 0.1 mm3 cm23, which grows to Va .1 mm3 cm23 under volcanic PSC conditions. For agiven aerosol volume the three curves in Fig. 2~a!reveal that the backscatter cross section ba decreaseswith wavelength approximately as l21.5 in the regionof background aerosol and as l21 under volcanic orPSC conditions.

Except for the 1064-nm case, errors of volume es-timates follow patterns opposite the surface-areaones. In the region of background aerosol, errors ofless than 25% point at volume estimates as moreaccurate than surface-area ones. However, dVayVavalues increase to 25–30% at 532 nm and to 35–45%at 355 nm under volcanic or PSC conditions. Con-versely, at 1064 nm volume estimates are affected byerrors lower than 20% starting from the backgroundaerosol region. However, observational errors limitthe quality of the estimates in this region at all wave-lengths. Altogether, model-dependent volume-estimate errors remain comparable with thosereported for in situ particle counters ~10–20% on av-erage17! at all wavelengths in the case of backgroundaerosol and at 1064 and 532 nm for volcanic or PSCaerosol.

C. Extinction-to-Backscatter Ratio

Average value points of the extinction-to-backscatterratio, Reb 5 sayba, and relevant errors dRebyReb as afunction of ba are plotted in Figs. 3~a! and 3~b!, re-


Table 2. Equation ~4! Coefficients of Parabolic Fits to the Average Value of the Aerosol Variables ~Var!,a as a Function of Backscatter Cross Sectionba ~cm21 sr21! at 355, 532, and 1064 nm

Run Var bmin bmax a0 a1 a2 c

355 Sa 0.42 3 10211 0.31 3 1027 3.4591 1.6680 0.0523 0.9998532 Sa 0.17 3 10211 0.23 3 1027 1.8671 1.3027 0.0335 0.9998

1064 Sa 0.10 3 10211 0.13 3 1027 1.5750 1.2096 0.0299 0.9993355 Va 0.42 3 10211 0.31 3 1027 0.6479 1.8241 0.0435 0.9999532 Va 0.17 3 10211 0.23 3 1027 20.1023 1.6415 0.0352 0.9999

1064 Va 0.10 3 10211 0.13 3 1027 20.3111 1.5656 0.0336 0.9999355 sa 0.42 3 10211 0.31 3 1027 24.9626 20.2740 20.0615 0.9997532 sa 0.17 3 10211 0.23 3 1027 24.8636 20.3123 20.0655 1.0000

1064 sa 0.23 3 10211 0.13 3 1027 22.9857 0.0074 20.0520 0.9997355 sayba 0.42 3 10211 0.31 3 1027 24.9413 21.2711 20.0615 0.9859532 sayba 0.17 3 10211 0.23 3 1027 24.9027 21.3221 20.0661 0.9940

1064 sayba 0.23 3 10211 0.13 3 1027 22.9390 20.9841 20.0516 0.9198355 reff 0.42 3 10211 0.31 3 1027 23.1071 0.0029 20.0156 0.9990532 reff 0.18 3 10211 0.24 3 1027 22.0104 0.2345 20.0028 0.9990

1064 reff 0.10 3 10211 0.13 3 1027 21.7146 0.2903 0.0009 0.9993

aSurface area Sa ~cm2ycm3!, volume Va ~cm3ycm3!, extinction sa ~cm21!, extinction-to-backscatter ratio sayba ~sr!, and effective radiusreff ~cm!. bmin and bmax ~cm21 sr21! define the region over which the fit was computed. Parabolic regression correlation coefficients cindicate the quality of the fit.

spectively. In Fig. 3~a! are also plotted as solidcurves the fits to Reb. These can be computed eitherdirectly by means of the fit constants provided inTable 2 for the variable sayba or according to

Reb 510~a0E 1 a1E log ba 1 a2E log2 ba!

ba, (6)

where the coefficients axE represent the constants ofthe second-order polynomial fit to the relationship saversus ba obtained by the model. These coefficients,which provide the link between aerosol extinctionand backscatter, are also reported in Table 2 as vari-able sa. Up to approximately ba 5 3 3 10211 cm21

sr21, values of Reb are fairly similar at all wave-lengths. Beyond that point the three curves sepa-rate, the ratio being smaller the shorter thewavelength. Maxima of approximately Reb 5 45, 50,and 60 sr are reached at 355-, 532-, and 1064-nmwavelengths, respectively. In the large cross-section limit all simulations converge to values of theorder of Reb 5 10–15 sr. Since the number of largercross-section points at both 1064 and 532 nm reducesto less than 100 sooner than at 355 nm, such behavioris mainly visible on the 355- and 532-nm curves. Inthe case of volcanic aerosol or PSC’s ~ba $ 1029 cm21

sr21 at 532 nm!, both 532- and 355-nm plots show Rebto decrease for increasing ba, matching well the av-erage Reb values at 532 nm reported by Jager andHofmann21 and the vertically resolved Reb profiles ofthe Mt. Pinatubo cloud obtained by Ansmann et al.24

at 308 nm, respectively. Overall agreement ofmodel results with the ones reported by both authorsis quite good. The 1064-nm run reaches its maxi-mum in the typical volcanic or STS PSC region, whiledecreasing for both background and heavy volcanicconditions. Under typical volcanic conditions, i.e.,R 5 2 at 532 nm and at 15 km, Reb would be 60, 40,and 23 at 1064, 532, and 355 nm, respectively. Such


differing behavior indicates that the choice of Rebvalues might play an important role when lidar ob-servations taken at different wavelengths are in-verted and compared. In terms of fitting-curvequality, the 532-nm one reaches the best approxima-tion and the 1064-nm one reaches the poorest. Infact, correlation coefficients reported in Table 2 showthat, with the ratio Reb being a composed parameter,the quality of parabolic fits to the relationship Rebversus ba is somewhat poorer than it is for the otherparameters.

Relative errors of Reb estimates presented in Fig.3~b! are generally less than 40% and tend to decreasebelow 30% under volcanic or PSC conditions. Atboth 355 and 532 nm, dRebyReb reduce to values aslow as 10–20% for heavy volcanic or ice particles.Altogether, model accuracy is consistent with the val-ues ~15–50%! that characterize direct determinationof Reb by means of the Raman lidar.24

D. Effective Radius

Points of average relationships between the distribu-tion effective radius reff and ba are plotted in Fig. 4~a!.Relevant errors dreffyreff are shown in Fig. 4~b!.When passing from background to volcanic or PSCconditions, reff undergoes a change from approxi-mately 0.15 to 0.6 mm. Such behavior is in goodagreement with a large set of observations made byseveral groups after the Mt. Pinatubo event.9 Whenrelated to backscatter, the distribution effective ra-dius shows an overall dynamical range of just over 1order of magnitude and a less regular behavior thanthat observed in the case of Sa or Va. However, thesecond-order polynomials provide fits @solid curves inFig. 4~a!# of good quality, which can be used as asmoothed estimate of the relationships. Relevantparameters of the fits are presented in Table 2. Un-der most aerosol conditions reff relative errors shownin Fig. 4~b! range between 40% and 55%, clearly in-


dicating the effective radius as the parameter suffer-ing the highest variability so far. In this respectlarge variability and small change between back-ground and volcanic PSC conditions make the distri-bution effective radius a parameter that is harder tohandle for the characterization of aerosol properties.

5. Comparisons with Observations

For performing a validation of the modeled relation-ships between ba and aerosol surface area and vol-ume at 355 or 1064 nm, two lidar profiles taken by the

Fig. 2. ~a! Average value points of the relationship Va versus ba

computed at 355 ~open triangles!, 532 ~crossed circles!, and 1064nm ~open squares!. Solid curves show the log–log, second-orderpolinomial fit to the relevant points. Fit parameters are reportedin Table 2. ~b! Solid curves with symbols show relative errorsdVayVa ~dVa 5 1s! of model estimates represented by the fits of ~a!.Single symbols depict typical observational errors at 355 ~filledtriangles!, 532 ~filled circles!, and 1064 nm ~filled squares!, asderived for the NASA Langley three-wavelength lidar.

NASA Langley three-wavelength, Nd:YAG lidar inMarch and December 199222 were employed. Theseprofiles, totaling approximately 200 data points, arerepresentative of the volcanic aerosol generated bythe June 1991 Mt. Pinatubo eruption. Since no con-temporary surface area or volume observations areavailable, the 355- and 1064-nm estimates are eval-uated against the 532-nm ones, whose quality wasalready checked in Gobbi.11 Figure 5~a! shows onthe same plot curves of the model-derived relation-ship Sa versus ba at the three wavelengths and pointsrepresenting the Langley observations. The rele-vant model error bars for surface estimates at both355 and 1064 nm are also plotted. Observations at

Fig. 3. ~a! Average value points of the relationship Reb versus ba

computed at 355 ~open triangles!, 532 ~crossed circles!, and 1064nm ~open squares!. Solid curves show the log–log, second-orderpolynomial fit to the relevant points. Fit parameters are reportedin Table 2. ~b! Relative errors dRebyReb ~dReb 5 1s! of modelestimates represented by the fits of ~a!.

532 nm are not shown, as they coincide with themodel curve and are employed only to estimate par-ticle surface area. Analysis of this data set revealshow 78% and 99% of the observations are includedwithin model-estimate error bars at 355 and 1064nm, respectively. In the case of particle volume,model estimates and observations were plotted inFig. 5~b!. This analysis shows that 89% of the355-nm observations and 43% of the 1064-nm obser-vations fall within model error bars. The pooreragreement at 1064 nm is mainly due to the estimates’expected errors being quite small and to a systematicdifference ~whose origin is difficult to attribute!between the model and the observations at this wave-length. In this respect note that variability intro-

Fig. 4. ~a! Average value points of the relationship reff versus ba

computed at 355 ~open triangles!, 532 ~crossed circles!, and 1064nm ~open squares!. Solid curves show the log–log, second-orderpolynomial fit to the relevant points. Fit parameters are reportedin Table 2. ~b! Relative errors dreffyreff ~dreff 5 1s! of model esti-mates represented by the fits of ~a!.


duced by observational errors was not included in theerror bars. Overall, the agreement between obser-vations and relevant estimates can be consideredgood in the case of surface area at 355 and 1064 nmand for volumes at 355 nm, and acceptable in the caseof volume estimates at 1064 nm.

6. Conclusions

Functional relationships for estimating stratosphericaerosol surface area, volume, extinction-to-backscatterratio, and effective radius from single-wavelength li-

Fig. 5. ~a! Curves of the model-derived relationship Sa versus ba

at the following three wavelengths: 1064 ~top curve with errorbars!, 532 ~middle curve!, and 355 nm ~bottom curve with errorbars!, plus single points representing two NASA Langley, three-wavelength lidar observations made in January ~filled symbols!and December ~open symbols! 1992. Observations at 532 nm arenot plotted and are employed only to estimate particle surface areaand coincide with the 532-nm model curve. Squares and trianglesrepresent the 1064- and 355-nm lidar backscatter observations,respectively. ~b! Same as in ~a! but for volume estimates.

dar measurements have been determined at each ofthe three Nd:YAG lidar wavelengths of 355, 532, and1064 nm. These relationships have been obtained bythe computation of Mie backscatter ba and extinctionsa for sets of 10,000 aerosol size distributions of vari-able composition, randomly generated according toboundary conditions derived from experimentally ob-served data. Simulated aerosol distributions accountfor worldwide stratospheric conditions ranging frombackground to postvolcanic sulfate particles and liquidpolar stratospheric clouds ~PSC’s!. Relevant equa-tions were derived from least-squares fitting of theaverage relationships between the investigated pa-rameters and aerosol backscatter. In log–log coordi-nates all relationships found are well approximated byparabolic curves. As a general rule aerosol backscat-ter showed an inverse relationship with wavelength,decreasing approximately as l21.5 in the region ofbackground aerosol and as l21 under volcanic or PSCconditions. Errors of the resulting optical modelrange between 10% and 50% for surface area, beingsmaller at shorter wavelengths and decreasing atlarger values of ba. Volume-estimate errors range be-tween 15% and 50%, being smaller at longer wave-lengths and increasing with ba only at 532 and 355 nm.Errors of extinction-to-backscatter ratio estimates re-main fairly constant in the 20–40% range as far as theheavy volcanic PSC condition, where they tend to de-crease to 10–20% at both 355 and 532 nm. At allwavelengths these errors are comparable with theones that characterize measurements obtained by op-erational direct techniques. Actual errors are ex-pected to be larger than model ones in the region ofbackground aerosol, where observational errors over-come model ones. Effective radius estimates sufferfrom a small dynamical range of the parameter andfrom relative errors of 40–55%. These conditionsmake reff a less favorable output of the model. Assurface area errors strongly decrease at larger back-scatter cross sections, i.e., in the presence of volcanicclouds and PSC’s, this model provides a good tool forestimating a parameter so important in ozone-depletion studies at each of the three wavelengths in-vestigated. Also, model estimations of aerosolvolume allow a fairly accurate evaluation of theirmass, particularly at longer wavelengths. Compari-sons of model results and actual three-wavelength li-dar observations have shown the model to fit observeddata within error bars in approximately 79% and 99%of the surface estimates and in 89% and 43% of volumeestimates at 355 and 1064 nm, respectively. At allwavelengths functional inference of the extinction-to-backscatter ratio allows a more realistic assumptionthan the constant value frequently employed in lidaranalysis. This can be particularly important duringinversion and comparison of lidar profiles at differentwavelengths, because the ratio Reb was shown to varyquite strongly. Finally, a comparison of both relativeerrors and fit quality at the three Nd:YAG laser wave-lengths points at the 532-nm one as the best suited forestimating stratospheric aerosol physical properties bymeans of single-wavelength, Nd:YAG laser radars.

This study was partly funded by the Italian SpaceAgency ~ASI!. The author is grateful to L. R. Poole,head of the NASA Langley aerosol research branch,who kindly provided three-wavelength lidar profilesfor validation of the model.

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parameterization of stratospheric aerosol physical properties on the basis of nd:yag lidar...

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