J. Aerosol Sei., Vol. 20, No. 8, pp. 1213-1216, 1989. P r i n t e d in Great Britain.
0021-8502/89 $3.00 + 0.00 Pergamon Press ple
REMOTE MEASUREMENT OF THE AEROSOLS SIZE DISTRIBUTION BY LIDAR
C. Flesiaa, H.J. Koelschb, P. Ralrouxb, J.P. Wolfo, L. WOstec a Instimt de Physique Thtorique de l'Universit6 de Lausanne, CH-1015 Lausanne, Switzerland Present address: Atmospheric Physics ETH, CH-8000 Zildch b Centre d'Applieations Laser, Ecole Polytechnique Ftdtrale, CH-1015 Lausanne, Switzerland c Institut f'ttr M0[ektilphysik, Freie Universit/lt Berlin, D-1000 Berlin
The purpose of this paper is the remote and spatially resolved measurement of the aerosols size distribution in the atmosphere and in particular of water droplets in clouds and fogs. The technique is based on the well-known baekscattering LIDAR (Light Detection and Ranging)  technique, using different wavelengths (598.8 rim, 299A rim) and a stochastic based inversion algorithm.
Water droplets play an essential role in atmospheric physics, especially in clouds formation. The clouds evolution is indeed characterized by two different phases [2,3]: 1) Condensation of water vapor into droplets until a typical size of 15 gin. 2) Coalescence of the droplets until the formation of rain. The degree of maturation is characterized by the water droplets size distribution, as a unique parameter. A direct measurement of this size distribution will then constitute an essential observation for more precise meteorological forecasts. However, to be relevant and suitable, this measurement must be done remote and in situ, which suggests the use of the LIDAR technique. A direct way to invert the LIDAR equation, and determine the aerosols size distribution, is to assume a relation between extinction and backscattering coefficients . However, this relation is determined empirically, and strongly depends on atmospheric conditions. Therefore, we developed a new algorithm based on the stochastic properties of the atmospheric aerosols, without any a priori condition on their size distribution. 2. Exvedmental In a LIDAR arrangement, a laser pulse is sent into the atmosphere, and one records the resulting backscattered light versus time (i.e. range). The laser backscattered light depends on the aerosols concentration in a similar way as a RADAR, but at different optical wavelengths. As an example, (fig. 1) shows the effect of the wavelength for different type of particles (aerosols, cloud and rain droplets). More precisely, the received number of photons from a distance R at a wavelength Z is given by (assuming that each photon is scattered only once ): R
M (R, ~,) -- Mo(~,) -A° n (R, X) AR ~(R,Z) exp ( - 2 | a (R', Z) dR')
Where Mo is the energy of the lasersource, A the collectingarea of the receiving telescope,R the distance from the Lidar unit,~ the overall efficiency of the receiving system, AR the verticalresolution,and o~, ~. the exfincion and backscatteringcoefficients.
C. FLESIA et al.
The experimental apparatus (fig. 2) is based on the previously described mobile LIDAR unit, which has been developed at EPFL since 1985 for pollution monitoring [5,6,7]. ilJ The laser system is based on an Excimer laser (Lambda Physik EMG 201 MSC) ~,~ of some 400 mJ/pulse (308 nm) at a repetition rate of 80 Hz, which pumps i , !t'~ alternately two dye-lasers (Lambda Physik FL 2002) where one is frequency ....I /, doubled, tuned respectively on L1 (598.8) and 9~2(299.4). The dye laser beams ....'~..'~_~_i::~:~/l are directed in the region of investigation by a fiat mirror, which can be moved in ...... elevation and azimuth. The same fiat mirror collects the backscattered light and .......i J directs it onto the 40 cm diameter receiver telescope. The detector used is an EMI ~': ! 9817 QB photomultiplier, especially selected by the manufacturer for its linearity. ] The output signal is preamplified, and digitized in 100 MHz - 8 Bits transient J..... . . . ...... ...... recorders (LeCroy TR 8818 A). The raw data processing and storage are assured ......i by a microcomputer (LeCroy 3500 SA). E 3. Th¢¢ry ....t] ~'i~, , . hti The expression of the extinction and the backscattering coefficients of the 0~t;~-_ I .... =::Y~'~_ LIDAR equation (1) are: I
*~c~(r) p(r) dr
13;.= f**Q x(r) p(r) dr
...... oo :"~ , ', (2)
"o", ~ : , ~
They are respectively functions of the extinction cross section ~, (r), the backsc- Fi~.1: Lidar signal at 598.8 attering efficiency Qx (r) and the size distribution p(r). nm (plain line) and 299.,1nm In particular, the shape of the probability distribution p(r) plays an essential role (dot.line).Top, no rain fall, on the transmission and backscattering properties of the random medium [ 8 ] . Therefore, the extinction and backscattering coefficients ff~.and 13x as functions of p(r) depend
bottom, continuous rain fall.
on the parameters which define the particle size distribution function. /. The characterization of the particles size ~ : : distribution involve the inversion of the lidar ~ i equation. Moreover, the accurancy of the results is "~'7~i____ directly dependent upon the sensitivity of the ~ ~ ] system to the physical assumptions, like boundary ~/ ~_., .~. "~ ~ values, or extinction-to-backscattering ratio. For this reason and because of the complexity of Fi2 2:1 powergenerator,la coolingdovice,2excimerpump the atmospheric system, the main advantage of an laser,2agas stoek,3abdye lasers,4 SHG:BBOcrystal,550% inversion algorithm is found in the fact that it only beamsplitter+chopper,6 b~am expander,7 filter,8 scama.mg uses the general properties of the particle size dismirror,9 tdescope,10 vidco+mortitor (option),t 1 receiverbox, tribution function.A complete method to study age- 1la iris,l tb lens,llf pm,12 transient digitizer,t3 computer, neric probability distribution function p(r) is to stu- 14 grphic display,15 data storage,16 plotter. dy the set of its moments Mj (j = 1, ~).In particular,M 1def'mes the main value of the random variable, and ( M2 - M12 ) defines its variance, p(r) is, in fact, completely characterized by its moments . In this way, it is possi.ble, without any restrictive assumption,to replace the expression of the particle size distribution p(r) in the def'mition of the extinction and backscattering coefficients ~ and ]3~.by an expression where the unknowns are the moments Mj of p(r).
Aerosol size distribution
This gives,for the coefficientsa~.and ~. at a given wavelength ~, [I0]. (Z~.= C 1 (~,) M I + c 2 (~,) M 2 + c3()~)M 3 + ....
[~= c'1 (~.)M 1 + c'2 (~,)M 2 + c'3 ()~)M 3 + ......
where the coefficientsc i (L) and C'i(k),of which the analyticalform is completely known, are respectively functions of the "extinctioncross section and the backscattering efficiency and their derivatives. The essential feature of this development is that the coefficients cj (Z.)and c'j (Z.) are independent of the particlesize and must be computed separatelyas functionsof the wavelength, while the moments Mj of p(r),which contain the dependence of the coefficients co).and [~).on the particlesize,are independent of ~,. This reduces the lidarequation (I) to a system of non-linearalgebraicequations where moments Mj ofp(r) are the unknowns. Moreover, the moments Mj are not independent themselves and the determination  of the number n of independent variables of such a system allows to determine, from the measurement of the backscattered intensityfor several wavelengths, the particlesize distributionwith an accurancy that depends only on the number n of equations. The lidarequation inversion and consequently the characterisationof p(r)must be carriedout for arbitrary small atmospheric layers (0, R) and must take into account local inhomogeneities. In fact, a renormalization process of the energy of the laserpulse M o from the knowledge of the calculated oh. and [Ix.allows then the reconstructionof the verticalprofilesof the particlessizedistributionand concentration. 4. Results A first test o f the inversion algorithm, using two wavelengths ( 598.8 nm and x.s~8om 299.4 nm ), has been performed on Lidar vertical profiles of a clear atmosphere -
containing a cumulus cloud at about 2 km height (fig. 3). The algorithm could therefore be tested on two very different aerosols size distributions, exhibited respectively by
1) Particles in the clear atmosphere at a height of 500 m above the lidar unit. 2) Particles inside the cloud at a height of 2100 m . The results for the particle sizes and concentration for these two experimental conditions are:
Clear A t m o s p h e r e Inversion Algorithm Standard Distribution
Mean Radius < a > = 0.47 Jan 0.1 lain to 1. larn
Concentration 32 part / cm 3 10 to 100 part/cm 3
Cumulus Inversion Algorithm Standard Distribution
Mean Radius < a > = 12.5 Jan 10 lain to 20 Jam
Concentration 4 part/cm 3 10 to 100 part / cm 3
Fig 3:raw data fromtheLidar
These first results are very satisfactory, considering that only two wavelengths were used. The mean value is, in particular, in good agreement with standard values. On the other hand, the particle concentration appears too low in the cloud, compared to standard atmospheric conditions. This effect is certainly due to multiple scattering processes, which occur only for large sizes and concentrations, and therefore do not affect the clear atmosphere measurement. Another possible contribution could be due to a smaller droplet density at the bottom of the cloud, a~d the measured average value referred to a layer located at 100 m above the cloud base. A direct comparison with classical analyzers is then crucial for a valuable check of the accuracy of the technique. AS 20:8-Y
C. FLESIA et al.
Improvements of the technique, involving more simultaneous wavelengths, are in progress. One will then be able to access higher order moments, and to increase accuracy on the mean value and standard deviation. Moreover, systematic investigations of the multiple scattering effects, as a function of the aerosols size and concentration, will be performed in a near future. References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.
"Laser Remote Sensing", R.M. Measures, J.Wiley & Sons ed., New-York (1984) "A Short Course in Cloud Physics", R. Rogers, Pergamon Press, Oxford (1979) "Cloud Physics and Weather Modi~cation", Y.S. Sedunov, Keter Publ., Jerusalem (1974). J.D. Klett, App.Optics 24 1638 (1985) J.P. Wolf, L. W6ste, Helv.Phys.Acta ~ 161 (1987) "Applications de la Spectroscopie laser ~ la Pollution Atmosphdrique", J.P. Wolf, Th6se de doctorat no 681, EPFL (1987) H.J. K61sch, P.Rairoux, J.P.Wolf, L.WOste, App. Optics 28 2052 (1988) C.Flesia, R.Johnston, H.Kunz, Europhys. Lett 3(4), 497 (1987) and C. Flesia,R. Johnston, H. Kunz, Phys Rev. A, October 1989 "Characteristic Functions", M.Lukacs, Griffin ed. (1970) C. Flesia, R. Calinon, submitted to Phys. Rev. A.