March 1980 / Vol. 5, No. 3 / OPTICS LETTERS 135

Lower-stratospheric aerosol microstructure investigation withmultifrequency lidar

E. V. Makienko and I. E. Naats

The Institute of Atmospheric Optics, Siberian Branch, USSR Academy of Sciences, Tomsk, USSR

Received July 12, 1979; revised manuscript received December 11, 1979

The results of investigation of the lower-stratospheric aerosol microstructure by the inverse-problem method basedon double-wave lidar sounding data at X = 0.53 and 0.694 gm are discussed. Assuming the aerosol refractive indexin the lower stratosphere to be close to the model values m = 1.43 and K = 0, the altitude profiles of aerosol micro-structure parameters at 14-25-km altitude were determined. An analysis of accuracy characteristics of aerosol mi-crostructure laser sounding of the lower stratosphere is presented.

To estimate the effect of stratospheric aerosol onsolar-radiation transfer, one should have systematicdata on the optical characteristics, concentration,size-distribution spectrum, and chemical compositionof the particles of the aerosol. Using multifrequencylaser sounding, based on the methods of optical mea-surement inversion, one can obtain information on theconcentration and the size-distribution spectrum, as-suming that the complex refractive index of particlesis known.

The inversion method is described briefly, and theresults are analyzed of the stratospheric aerosol mi-crostructure determination obtained by the authors,using the inversion method of the double-frequencylaser sounding data. The initial information is the al-titude profiles of the backscattering aerosol coefficientsmeasured with ground-based lidar (obtained at Tomsk,summer 1975). Technical characteristics of the mea-suring complex and the methods of determining thealtitude profiles f3,G\,Z) are given in Ref. 1. Aerosolmicrostructure was defined by the method of modelestimates suggested earlier by the authors2 and in-tended for interpreting the optical characteristicsmeasured using two and three wavelengths. In thismethod, one estimates separate parameters of aerosolmicrostructure, such as the distribution mode r, in theparticle-size distribution, the mean radius, the con-centration N, the total geometrical cross section S, andthe proper volume of particles per unit-scattering vol-ume of a medium. It is assumed a priori that the ana-lytical form of the required distribution and the re-fractive index of the aerosol substance are known.

We shall consider briefly the computational schemeof the method, assuming the inverse problem solutionto be among the single-mode functions. As an example,one can use the four-parametric gamma distribution

n(r) = ara exp(-br7) (1)

recommended in Ref. 3 as a model for the particles ofstratospheric aerosol. Let us assume that the param-eters S = f wrr2n(r)dr and the distribution mode rGof the function G(r) = 7rr2n(r) are required to be esti-mated by measuring #,B(X) at four wavelengths (0.345,

0.53,0.69, and 1.06 gm). Since there is little initial in-formation in our formulation of inverse problem, theparameters a and y in Eq. (1) are chosen a priori, using,for example, recommendations in Ref. 3. For the dis-tribution, Eq. (1), the backscattering coefficient can becalculated by the following formula:

flr*(X) = SK.(X) = S j' Kr(rX)co(r)dr, (2)

where K7 (rX) is the efficiency factor of backscatteringaccording to the Mie theory in the assumption of scat-tering particle sphericity,

(a + 2 (a + 3)/y

sn(r)=r~(a +33rGP(

x(I{ exp - 2(~r)j| . (3)

Let us choose the wavelength Am, for which themeasured characteristic #fl(X) is maximum, and thenproceed to the normalized values 3(Xi)/I3(Q). Because/3(Ai)/0(3\.) = k(Xi)/k(Am), this method allows theparameters S and rG to be estimated separately. Forexample, the value rG* can be determined by mini-mizing the following difference:

P(rG) = I [:(,)- K(> --|. (4)p ir=,tff(X ) K(X., rc)I2

This value rG* calculated from Eq. (4) is then used todetermine the parameter S* according to the. formulain Ref. 2,

S* =f(Xi) K(Xi, rG*)

i=1(5)

E2 K(Xi, rG*)i=1

The authors used the minimizing methods of thefunctions of many variables, e.g., the method of steepestcoordinate descent. When the parameters S*, rG*, a,and y are known, it is easy to define other characteris-

0146-9592/80/030135-03$0.50/0 ©) 1980, Optical Society of America

136 OPTICS LETTERS / Vol. 5, No. 3 / March 1980

4 (A) KMrn.i~~~. 0I ' X 6 0 I

04 OS 08 A,,.,,

10

(6)

02 0304 05 a,um

Fig. 1. Influence of the error in /3,(X) on the resulting in-version distribution in the numerical experiment: (a) initialvalues 0,(X), (b) inversion distribution n(r).

Table I. Percentage Errors in Estimates of Size-Distribution Parameters

Particle Radius ro (mm) 0.1 0.15 0.2 0.4

Estimated Error Es (r > ro) (%) 20 15 10 20EN(r > ro) (%) 40 15 15 20

tics of microstructure, e.g., the distribution mode r,particle concentration, and proper volume of particles.The scheme of calculations remains the same if anotherdistribution is chosen as a model of the size spectrum.For example, for the Junge distribution n(r) = arv-, theparameters S and v are defined using an analogousprocedure. In this case, as is shown in Ref. 2, it ispreferable to use the following modification in Eqs. (4)and (5):

n(r) = Jai,la2r -e -r/R1 '

0 s r < R1,R, -< r < -'

0.53, 0.69, and 1.06 Am with the 10% amplitude of themaximum value of f 7(X) in a given spectral range; Fig.1(b) is the resulting inversion for the distribution n(r)from the inversion of optical characteristics [Fig. 1(a)].From Fig. 1(b) it is seen that the influence of measure-ment errors is more essential when reconstructing n(r)at limit points of the solution interval. The corre-sponding errors in the estimates of size distribution ofintegral parameters S(r > ro), N(r > ro), where ro is afixed radius of particles, for solution 2 in Fig. 1(b) aregiven in Table 1.

It should be noted that, for the indicated set of op-erating wavelengths, there is a certain effective parti-cle-size interval within which the errors of restitutionare minimal, and these intervals are compared withthose of truly optical measurements. In this example,such an interval is the range of radii 0.2-0.5 Am [Fig.2(b)].

Below we give an example of application of themethod considered to evaluate the mean parameters ofstratospheric aerosol microstructure obtained from lidarmeasurements of the altitude profile i3,(ZX) [Fig. 2(a)]for the wavelengths X1 = 0.53 Am and X2 = 0.694 Am(Tomsk, June 15, 1975, Ref. 1). The parameters S andrG were determined according to Eqs. (4) and (5) basedon the model distribution at given values of av = 2 and-y = 0.7. The residual characteristics of aerosol givenin Figs. 2(b)-2(d) were calculated using the set of pa-

25

'~20

(6)

This distribution is close to Junge's at A > 4 and withthe particle size 0.1-2 im. At the same time, the regiondefined by parameter ,u is much wider than that definedby parameter v, which is important in the algorithms forminimizing the difference [Eq. (4)].2

Stability of this method of interpretation to randomerrors in the initial data is illustrated by the numericalexamples of Fig. 1. Figure 1(a) denotes the opticalcharacteristic it(X) (curve 1) corresponding to the sizespectrum model haze H,3 along with the refractive indexm = 1.5, K = 0. Curve 2 is obtained from Ref. 1 byoverlapping the oscillating perturbation at X = 0.345,

'5

I- , i ,,

0 J 70-3 2 40 -3

S. ,¢ -14� , Kar' 5r'

, 20

r~ /in Nv r > N .1i5), cm -3

Fig. 2. Altitude profiles I3,(ZX), Tomsk, June 15,1975 (Ref.1), and the results of interpretation.

Table 2. Dependence of Particle-Size Distribution Reconstruction Accuracy on Refractive Index for DifferentAltitudes

AltitudeDistribution S(r > ro) 10-3 (km-'), ro (pm)

Z Mode N(r > ro) (cm- 3 ), ro (gm) N(r > 0.15) Es Es es(km) r,, (pm) 0.15 0.2 0.25 N(r > 0.25) 0.15 (%) 0.2 (%) 0.25 (%)

14.25 0.12 0.07 2.5 5.8 1.9 3.2 1.5 1.7 1.7 3.4 0.88 1.11 21 0.82 0.87 6 0.75 0.63 1615.75 0.11 0.07 4.3 8.7 3.1 4.8 2.2 2.6 2.0 3.4 1.38 1.66 16 1.27 1.29 2 1.12 0.94 1617.25 0.11 0.07 5.5 11.2 4.0 6.2 2.8 3.3 2.0 3.4 1.77 2.13 16 1.63 1.66 2 1.44 1.21 1618.75 0.11 0.07 6.1 12.1 4.4 6.8 3.1 3.7 2.0 3.4 1.98 2.34 15 1.82 1.83 1 1.61 1.35 1620.25 0.11 0.07 5.5 11.3 4.0 6.2 2.8 3.3 2.0 3.4 1.77 2.15 17 1.63 1.67 3 1.44 1.22 1521.75 0.22 0.18 0.36 0.45 0.32 0.39 0.28 0.32 1.3 1.4 0.32 0.29 10 0.32 0.28 11 0.31 0.27 1223.25 0.20 0.16 0.24 0.29 0.21 0.24 0.18 0.2 1.3 1.4 0.18 0.16 12 0.18 0.16 13 0.17 0.15 1524.75 0.11 0.07 1.5 3.0 1.1 1.7 0.8 0.9 2.0 3.4 0.48 0.58 17 0.44 0.45 2 0.39 0.33 15

0075

0070

0005

Ill , ,, i..''I0 53 (a) 25.

0.604 1 20

tn-5 4n-'

March 1980 / Vol. 5, No. 3 / OPTICS LETTERS 137

/5 2, 0 t521 4 /,p- 05

ts5 o 4 0

t8-5 Ap-4 71 3 5

23 20(C) d

E 2 0 3 20 0 S r

13 15~~~~7 3

Fig. 3. Altitude profiles (3,(Z,X), Tomsk, June 14, 1975 (Ref.1). (a) 23 h 00', (c) 23 h 30', (b) and (d) profiles of particleconcentration.

rameters S, rG, q, and -y. The solution is given for a realpart of the refractive index m = 1.43 and an imaginarypart K = 0. These values of optical constants of theparticle substance are usually used in the analysis oflidar measurements and are based on the representationof particles of the sulfate layer of the lower atmosphereas spherical drops of an aqueous solution of sulfuricacid. The effect of errors in the real part of the re-fractive index on the restitution accuracy is shown inTable 2, in which the values of main microstructurecharacteristics are compared. These values are ob-tained from the inversion of the same initial data [Fig.2(a)] for m = 1.43 and m = 1.46 (the first and secondnumbers of the column, respectively). The resultsgiven in Table 2 show that the errors A m = 0.03 withP,3 inversion at wavelengths Al = 0.53 ,um and X2 = 0.694gm displace markedly the estimates of particle con-centration first of all for small particles with r • 0.2 Am.This effect is less noticeable for the particles whose sizeexceeds 0.2 gum [Table 2, N(r > 0.25)1. Taking intoaccount the effect of measurement errors on the accu-racy of determination of particle concentration (Table1), one can assume that if a chosen value m* = 1.43 forthe aerosols of the lower stratosphere differs from thereal one by the value Am - 0.03, then the correspondingerrors in the estimates N(r > 0.2) will be compared withthose that are due to measurement errors (,>10%). Todetermine the particle concentration with the radiusmore than 0.15 rm, the accuracy of assignment of m atthe same accuracy of initial data must be higher. Itshould be mentioned that strong dependence of re-construction errors on those of a priori choice of opticalconstants of the substance is typical, first of all, for theparticle concentration. Under the same experimentalconditions, the definition of a total geometric cross

section and corresponding parameters can be guaran-teed with great reliability. This is confirmed by theanalogous calculations given in Table 2. The errors inthe estimates of values S(r > ro) that are due to thedisplacement of the refractive index, on the average, bythe height, are 15%. Knowledge of the function S(r) issufficient for the solution of various problems of appliedoptics connected with radiation transfer in the atmo-sphere. The values of the aerosol parameters given inFig. 2 are typical when interpreting lidar measurements(Tomsk, June 1975), and they represent the mainregularities of altitude distribution of aerosol particlesin the lower stratosphere observed by direct methodsof concentration measurements for 1975-76. A char-acteristic property of the results obtained is frequentrepetition of the values of distribution mode r - 0.1,um. In a series of cases in the altitude range of 18-25km, the rn estimates obtained were shifted from 0.1 upto 0.2-0.25 gim, as seen in Fig. 2(c). Similar transfor-mation of the particle-size spectrum was observed onthe basis of the 1976-77 average data of filter mea-surements, 4 in a moderate zone at 12-21-km height. Acomparison of the particle-concentration altitude pro-files given in Figs. 2 and 3, obtained at m = 1.43 by themodel estimate method from the measurements of ,BA1 (X)for a short time interval, shows a noticeable space-timevariation of aerosol particle content in the lowerstratosphere. At the same time, in the layer of maxi-mum aerosol scattering at the 17-19-km height, theaverage value (June 15-16,1975) is within 3.5 to 4 cm-3 ,which satisfies the results of this value measurement bya photoelectric particle counter based on the data inRef. 5.

The results presented indicate a sufficient efficiencyof the laser sounding methods in the problem of remoteprobing of atmospheric aerosol microphysical charac-teristics.

References

1. V. E. Zuev, N. V. Kozlov, E. V. Makienko, I. E. Naats, andI. V. Samokhvalov, "Some results of sounding of strato-spheric aerosol microstructure by a multifrequency lidar,"Izv. Akad. Nauk SSSR, Fiz. Atmos. Okeana 13, 648-654(1977).

2. E. V. Makienko and I. E. Naats, "Problems of optimal es-timate of parameters of aerosol particle size distributionfrom optical measurements," in Atmosfernaya Optika(Nauka, Moscow, 1974), pp. 186-191.

3. D. Deirmendjian, Electromagnetic Scattering on SphericalPolydispersions (American Elsevier, New York, 1969).

4. H. H. Farlow, G. V. Ferry, H. Y. Lem, and D. M. Haves,"Latitudinal variations of stratospheric aerosol," J. Geo-phys. Res. 84, 733-743 (1979).

5. K. Ya. Kondratiev, ed., Atmospheric Aerosol and Its In-fluence on Radiation Transfer. On the Results of theSoviet-American Aerosol-Radiation Experiment (Gi-drometeoizdat, Leningrad, 1978).