raman lidar observations of cloud liquid water

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aman lidar observations of cloud liquid water

incenzo Rizi, Marco Iarlori, Giuseppe Rocci, and Guido Visconti

We report the design and the performances of a Raman lidar for long-term monitoring of troposphericaerosol backscattering and extinction coefficients, water vapor mixing ratio, and cloud liquid water. Wefocus on the system’s capabilities of detecting Raman backscattering from cloud liquid water. Afterdescribing the system components, along with the current limitations and options for improvement, wereport examples of observations in the case of low-level cumulus clouds. The measurements of the cloudliquid water content, as well as the estimations of the cloud droplet effective radii and number densities,obtained by combining the extinction coefficient and cloud water content within the clouds, are criticallydiscussed. © 2004 Optical Society of America

OCIS codes: 010.3640, 010.7340, 280.3640, 290.1090, 290.1350, 290.5860.

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. Introduction

loud physical properties are quite important in de-ermining the climate sensitivity to either natural ornthropogenic forcings because of their effect on ra-iation and their role in the hydrological cycle. Theloud liquid water content is one of the main param-ters for the assessment of water cloud microphysicsn a number of atmospheric studies �i.e., global cir-ulation models and aerosol radiative forcings�, be-ause it is directly associated with the cloud dropletumber density. In the last Intergovernmentalanel on Climate Change report it is also written that

. . . handling the physics and�or the parameteriza-ion of clouds in climate models remains a centralifficulty. There is a need for increased observa-ions . . .”.1 Here we investigate the capabilities ofn UV Raman lidar in measuring the liquid waterontent in low-level tropospheric clouds. Whitemannd Melfi2 suggested that “. . . an improved �Raman�echnique . . . would be to measure Raman scatteringrom liquid water in a portion of the liquid spectrumhat does not overlap the vapor signal . . ..” Startingrom this we designed a lidar receiver for simulta-eous detection of the Rayleigh–Mie backscattered

ight and of the photons Raman-backscattered by at-ospheric N2, H2O vapor, and liquid water. This

The authors are with the Dipartimento di Fisica, Universitaegli Studi L’Aquila, Via Vetoio Localita Coppito, 67010 L’Aquila,

taly. V. Rizi’s e-mail address is [email protected] 24 November 2003; revised manuscript received 8 July

004; accepted 14 July 2004.0003-6935�04�356440-14$15.00�0

a© 2004 Optical Society of America

440 APPLIED OPTICS � Vol. 43, No. 35 � 10 December 2004

equires that the detector unit perform an efficientpectral discrimination. In the actual setup, our UVidar allows a reliable estimation of the water vapor,erosol backscattering, and extinction and of the liq-id water in low-level tropospheric clouds.In Section 2 we report a short summary of the

aman spectral features of atmospheric water in theas and liquid phase; the lidar system �UV lidar at’Aquila, Italy, 42.35N, 13.22E, site elevation 683-msl� and the detector efficiency are accounted for inection 3. The Raman lidar theory and the tech-ique for the retrieval of cloud parameters are out-

ined in Section 4. Sections 5 and 6 are dedicated tohe measurement performance of the cloud liquid wa-er mixing ratio profile and to the summary and con-lusions, respectively.

. Raman Spectra of Water Vapor and Liquid Water

he molecular light scattering spectrum in the atmo-phere shows different components that are indicateds a Rayleigh scattering component �elastic Ca-annes lines plus the contribution of inelastic pureotational Raman scattering, which falls close to Ca-annes lines� and a Raman scattering component,hich includes the inelastic rovibrational Ramanands. In vibrational Raman scattering �for whichhe scattered radiation has suffered a frequency shifthat is characteristic of the stationary energy statesf the irradiated molecule�, the cross section is ap-roximately 3 orders of magnitude smaller than theorresponding Rayleigh cross section.

The Raman spectroscopy enables a trace constitu-nt to be both identified and quantified relative to theajor component of a mixture. The Raman shift of
certain molecule depends on its vibrational and

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otational energy and, therefore, on the structure, thetomic distance, and the atomic weight of the mole-ule. As an example, the nitrogen and oxygen mol-cules �whose atmospheric mixing ratios are constantnd known� show Raman shifts �vibrational–otational transitions� of approximately 2327 and556 cm�1, respectively.The water molecule has three degrees of vibra-

ional and rotational freedom. The three possibleibrational motions are labeled �1 �symmetrictretching mode, �3657-cm�1 energy�, �2 �1595-cm�1

ending mode�, and �3 �3756-cm�1 asymmetrictretching mode� and are often called the normalodes of vibration of the molecule. The water mol-

cule is an asymmetric top molecule that can alsootate. Hence the degeneracy in the vibrational andotational states is lifted resulting in many allowedransitions, which give rise to spectra with no readilyiscernible structure.

. Raman Spectrum of Water Vapor

he Raman spectrum of H2O in the gas phase can beimulated by use of the theory of rotational Ramanntensity of vibrational bands in asymmetric tops.igure 1 shows this spectrum calculated for unpolar-

zed radiation according to the parameterizationiven by Avila et al.3 �more details about our calcu-ations are available in Ref. 4�. The Q branch �pureibrational �0 3 �1� represents 82% of the full spec-rum, 5% �of the full spectrum� is into the rotationalings, and the rovibrational component of the �03 �3

ransition accounts for approximately 13%. The �0�2 transitions have been neglected; therefore, the

ain feature of the H2O Raman spectrum in the gashase is caused by the O–H bond stretching vibra-ion.

Currently, the best value of the Raman water va-or differential cross section, assuming 351 nm for anxciting wavelength ��0� and a 1��4 dependence, is

ig. 1. Raman spectrum of H2O in the gas phase. The spectrums almost independent of the atmospheric water vapor tempera-ures. The intense pure vibrational line has been cut to show theovibrational structures of the spectrum.

hat reported by Penney and Lapp,5 �8��20%� H

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0�30 cm2 sr�1, and the best value for the ratio be-ween Raman water vapor and nitrogen cross sec-ions is 2.5 � 10%.

. Raman Spectrum of Liquid Water

he Raman spectrum of bulk liquid water is quiteifferent. The O–H bond in H2O molecules is af-ected by the bulk hydrogen bonds that increase theistance between O and H in a water molecule. Thisffect decreases the energy of the O–H stretchingibration and reduces the Raman shift. The liquidater spectrum is much wider than the H2O Raman

pectrum in the gas phase. A possible reason for theroadening lies in the superposing contributions oftretching vibrations of water molecules combinednto clusters of a finite set of types and sizes.

Most of the authors who reported observation ofiquid water Raman spectra �i.e., Walrafen et al.6 andolenko et al.7� focused mainly on explaining the

tructure of liquid water from its manifestations inaman spectra. For the purpose of this work, wesed the model suggested by D’Arrigo et al.8 to sim-late the Raman spectrum of bulk liquid water.4he spectrum can be divided into three parts: thepen and closed components that are due toonhydrogen-bonded and hydrogen-bonded interac-ions in water, respectively, and a contribution aris-ng at low temperatures �e.g., supercooled region�hat can be attributed to the existence of ice as aeterophase fluctuation. Our formulation of theomponent model seems to represent the main fea-ure of the observations.9 In Fig. 2 it is evident thathe liquid H2O Raman spectrum is quite sensitive toemperature, which should be taken into account forhe atmospheric measurement of cloud liquid waterontent. In addition, qualitative comparison of the2O Raman spectra in the gas phase �Fig. 1� and in

he liquid phase �Fig. 2� shows that, to some degree,here is an overlap region between the two bands.

Several investigators10–14 have measured the dif-erential Raman scattering cross section of liquid

ig. 2. Raman spectrum of liquid H2O for unpolarized light atifferent temperatures.

2O mainly at the excitation wavelength of 488 nm.

0 December 2004 � Vol. 43, No. 35 � APPLIED OPTICS 6441

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hey determined that the value varies between �8 0�30 and �5 10�29 cm2 sr�1, and the dependencef this parameter on the Raman emission wavelengthlso varies from 1��4 and 1��5. Ahmad and Iles15

easured the absolute differential Raman scatteringross section of liquid H2O for a large interval ofxcitation wavelength �200–450 nm�, and their crit-cal review of the available data on the Raman crossection highlights large discrepancies. From theata of Ahmad and Iles,15 the best estimation of theifferential Raman scattering cross section of liquid2O at an excitation wavelength of 351 nm is ��6.5 �.7� 10�29 cm2 sr�1.

. Liquid Water in Cloud Droplets

n clouds it is expected that Raman scattering is due toater droplets, a situation that is quite different from

he case of Raman scattering from bulk liquid H2O.ropospheric clouds have a total �spherical� dropletumber density that can vary from a few to hundredsf droplets per cubic centimeter, the droplet radii alsopan a wide range from �0.1 to �50 m. The differ-nces between Raman scattering by molecules embed-ed in spheres with radii multiples of the excitationavelength and scattering by molecules in the bulkhase are evident in the scattering phase function16

nd manifest in the presence of resonance structuresn the spectral distribution of scattered radiation.17 Aetailed discussion of these effects is not an objective ofhis paper, therefore we refer to Whiteman and Melfi2

nd Melfi et al.18 for atmospheric applications. Ve-elovskii et al.19 performed numerical simulations ofnelastic scattering by microspheres with the use of aipole model. They concluded that “. . . the Ramanackscattering cross section does not depend signifi-antly on droplet size, and that the backscatteringrom droplets exceeds the corresponding value for bulkater by approximately a factor 2.” Furthermore, theain result applies to the intensity of Raman scatter-

ng by an ensemble of spheres of different sizes, whichs proportional to the droplet volume, as well as to themount of liquid water in cloud droplets.

. Lidar Setup

. Transmitter

n excimer laser is the source of the laser pulses.

Table 1. Las

Parameter

XeF excimer laserGas mixture

ResonatorPulse energyPulse repetition rateBeam divergence �full angle 50% of energy�Pulse durationBeam shape and dimension �vertical horizontal�

he laser technical specifications are reported in Ta- s


le 1. The laser output spectrum demonstrates theypical B 3 X electronic band transitions for threeines at 348.75 � 0.15, 351.05 � 0.15, and 353.25 �.15 nm with relative intensities of 10%, 50%, and0%, respectively.These measurements were obtained with a Jarrel-

sh 50-cm scanning spectrometer with a 1180-ine�mm grating, a 100-m slit width, and the line’sntensities were collected with a silicon photodioderray �Princeton Applied Research Corp. Model453A�. The overall instrument resolution was ap-roximately 0.01 nm. We did not investigate theependencies of the laser line intensities as a func-ion of the gas fill’s age and discharge voltage. Thebserved output intensities were stable over a timeeriod of several hours �less than one million laserhots�, and our estimation is in agreement with theesults of Burris and Heaps20 and with those ofhiteman et al.21 The emitted laser pulses were

irected into the atmosphere �zenith direction� with a-in. �5-cm� steering mirror with a pointing sensitiv-ty of approximately 0.1 mrad.

. Detector Unit

he general requirements for a detector unit can beummarized as follows:

range of altitudes to be sampled from the ground to000 m;optimization for the detection of weak Raman back-

cattering by N2, water vapor, and cloud droplet liq-id water;suppression of background light; andsuppression of cross talk among the different chan-

els.

These conditions impose restrictions on the choicef receiving optics �telescope� and on the design ofichroic beam splitters �BSs� and interference filtersIFs�. They also impose the use of notch filters �NFs�o provide an additional suppression of the stronglastically backscattered light in Raman channels.In our system the backscattered light is collected

y a zenith pointing telescope �Table 2� coupled with�5-m-long� optical fiber to transport the light to theetection box. Optical calculations show that theiameter of the laser beam spot image at the tele-

aracteristics

Specifications

Lambda Physik EMG 150 MSC GermanyHigh purity, Xe �20 hPa�, F2�5%��He�200 hPa�, Ne �2480 hPa�Unstable20–50 mJ �unpolarized�80 Hz �nominal�, 30 Hz �operative��0.4 mrad�20 ns21 mm 6 mm

er Ch

cope focus is less than 1.5 mm over the altitude

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ange above 300 m, and the central obstruction inhis range casts a shadow with a less than 0.03-mmiameter �we assume that the laser divergence is fourimes the manufacturer’s specifications�. In sum-ary, if the laser and telescope optical axes are par-

llel to within �0.5 mrad, the maximum imageiameter at the telescope focus is 4 mm. The opticalber �multimode silica with high OH content and theransmission ranges between 0.82 at 350 nm and 0.95t 410 nm� has a core diameter of 1.5 mm, a numer-cal aperture of 0.39, and it is coupled to the telescopeith an antireflection-coated �99% transmission in

he range between 350 and 410 nm� aspherical lens11.0-mm focal length, 5.5-mm clear aperture, 0.25umerical aperture�. This end of the optical fiber isositioned at the focus of the telescope and allows uso collect the full laser beam spot image.

The fiber transports the return light to the four-hannel beam separator �Fig. 3�, the light beam isollimated by a 1-in. �2.54-cm� plano–convex lens25.4-mm focal length, 99% transmission antireflec-ion coated over the 350–450-nm range� positioned inront of the bare end of the optical fiber. The max-mum beam spot diameter along the optical path inhe beam separator was approximately 40 mm, andhe angular dispersion was less than 0.03 rad.

The BSs are used at an angle of incidence of 45°;

Table 2. Receiver T

Parameters

Parabolic mirrorCoatingDiameterCentral obstruction diameterFocal length

ig. 3. Optical layout of the receiver’s beam separator: L, a 1-in.2.54-cm� plano–convex lens; BS, dichroic beam splitters; IF, ND,F, and PMT, the 2-in. �5-cm� interference filters, the interchange-ble neutral density filters, the notch filters, and the photomulti-liers, respectively. The spectral features of each channel can beabeled by a representative wavelength: 351-nm Rayleigh–Miehannel, 382-nm nitrogen Raman channel, 393-nm liquid water
aman channel, and 403-nm water vapor Raman channel.
1

he IF, NF, and neutral density �ND� filter are atormal incidence. Since the angular dispersion ofhe light beam is less than 2°, unwanted shifts of theichroic BS and IF spectral features are negligible.he main characteristics of the filters and BSs can bebtained from the manufacturer �Barr Associates,nc., Westford, Massachusetts�. BS#2 is a bareused silica plate with approximately 90% transmis-ion. The ND filters can be positioned in front of theFs to reduce the light intensity to avoid the satura-ion effects and signal-induced noise of the photomul-iplier tubes �PMTs�. After passing the final stage ofhe beam separator unit �i.e., IFs� the light is col-ected by a PMT �see Table 3�.

The voltage pulses at the output of PMTs are am-lified ten times by a fast preamplifier �EG&G Ortecodel 9305�, the discriminator reduces the dark

ounts, and finally the pulses are detected by a high-peed multichannel scaler �EG&G Ortec, Turbo-CS, max counting rate 150 MHz, no dead time� and

tored and displayed on a personal computer afterumming a number of laser shots. The typical timeindow is 200 ns, which corresponds to a spatial

esolution of 30 m. The maximum counting rate isept below 10 MHz, so the pulse pileup effects can beeglected. A pulse generator drives the laser andhe data acquisition chain. The start-up triggerulse is sent to the multichannel scaler and, after aelay of approximately 2 s, to the laser.

. Detector Efficiencies and Performances

he relative transmission of different channels is re-orted in Fig. 4. The spectral features of the di-hroic beam splitters and the interference and NFsllow a quite efficient spectral discrimination of back-cattered photons. A schematic of the full spectrumf lidar returns �not representative of the real signalntensities� is shown in Fig. 5. Most of the N2aman-scattered photons can be found between 377nd 387 nm, and the typical water vapor and theiquid water Raman spectra show a region of overlap.

ope Characteristics

Specifications

Marcon Costruzioni ottico-meccaniche ItalyMg2F � Al20 cm5 cm60 cm

Table 3. Photomultiplier Characteristics

Parameter Specifications

9214QA Thorn EMIDiameter of photosensitive area 46 mmDark current 5 nAQuantum efficiency 26%Typical gain 8 106

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The contribution of the ith species �i.e., air mole-ules and aerosol, N2, water vapor, or liquid water� inhe jth lidar channel can be evaluated according toji � �j��Ii��d�, where Ii�� is the normalized

ig. 4. Wavelength-dependent relative transmissions of the beameparator. The curves were estimated by use of the manufactur-r’s data sheet and the specifications of the various componentsfilters, mirror, lenses, optical fiber, etc.�.

ig. 5. Schematic of the Rayleigh–Mie and Raman components ofhe returned light spectrum. The Rayleigh–Mie part is the laserpectrum that has been measured �see Subsection 3.A�; the Ramanhifts of the different species were calculated as described in Sec-ion 2; and taking into account the laser spectrum, the differentaman bands were plotted on the wavelength scale. The maxi-um of each spectrum has been normalized to unity, and theavelength resolution is 0.04 nm.

Table 4. Optical Transfe

Channel Efficiency Air and Aerosols

�ch#1 �molecular� 8.33 10�7

�ch#2 �N2� 4.28 10�17

�ch#3 �water vapor� 9.56 10�22

�ch#4 �liquid water� 1.64 10�19 3.20


ackscatter intensity of the ith species, and �j�� ishe relative transmission of the jth lidar channel �Fig.�. The optical transfer matrix �j

i for the detectorox is reported in Table 4 �the actual setup of theeutral density filters has also been considered�.e can discuss the possible cross talk among the

ifferent channels �i.e., which fraction of the elasti-ally scattered photons can be found in the Ramanhannels�. For this purpose we consider that theignals collected by the lidar receiver are approxi-ately proportional to the relative concentration of

he ith species and to the corresponding relativeackscattering �Rayleigh or Raman� cross section.In a clear troposphere we can assume that the

elative abundance of N2 is 78% in volume, the liquid2O mass mixing ratio is approximatley 5 10�3g�

kg of air�, and the H2O vapor concentration is 5 g��kgf air�; and the Raman and Rayleigh differentialackscattering cross sections �d��d�� scale as fol-ows:

d�RamanN2

d�� 10�3 d�Rayleigh

d�,

d�RamanH2 O vapor

d�

� 3d�Raman

N2

d�,

d�Ramanliquid H2 O

d�� 15

d�RamanH2 O vapor

d�.

aking into account the spectral transmission �seeable 4� of the different channels, we determined that

the signal in channel #1 �air and aerosol, Rayleigh�ie scattering� is, in the worse case, contaminated100 parts in 1012 by the other contributions;the unwanted signal in channel #2 �N2, Raman� is1 part in 106;in channel #3 �H2O vapor, Raman� the liquid H2O

aman scattering contributes to the signal in anmount less than 1%, the other backscattered pho-ons constitute �20 parts in 109 of the total;

in channel #4 �liquid H2O, Raman� �2�100 of theignal could be due to H2O vapor Raman scattering,he contributions of the other scattering species areess than �5�1000.

In the presence of a low-level cumulus cloud, withliquid water content of approximately 0.5 g�kg of

ir, the efficiencies of the Rayleigh–Mie and N2 Ra-an channels remain similar. On the other hand,

n the H2O vapor Raman channel, a significant frac-

trix of the Detector Box

Raman

N2 H2O Vapor Liquid H2O

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ion of the signal is due to the liquid H2O, whereas inhe liquid H2O Raman channel the portion of theignal induced by the other species is �1�1000.However, laboratory tests of the detector indicate

hat the contributions of other scattering moleculesn the liquid water channel can be neglected. Weollected signals in four different configurations ofhe liquid H2O channel in two situations: during aight �31 July 2001� with stable and clear-sky con-itions and on 21 September 2001, in the presencef a low-level cumulus cloud. The reference con-guration is the operational setup; in the others wedded, in front of channel #4, IFs similar to those inhannels #1, #2, and #3, which suppress the liquid2O scattering and eventually indicate the pres-

nce of unwanted contamination from Rayleigh–ie or Raman scattering of the other species. The

esults are summarized in Fig. 6. This test indi-ates that no contributions from other scatteringolecules contaminate the liquid water channel.n the other hand it is expected that some percent-ge of the signal in channel #3 �water vapor� is dueo the eventual presence of liquid water. This waslso quite evident in the previous setup of the re-eiver.22

In summary, a relative fraction f�l ��0.11� of the

iquid water spectrum is collected in the water vaporhannel, and a negligible fraction, fl

� ��0.0002�, ofhe water vapor spectrum contributes to the signal inhe liquid water channel.

. Data Evaluation

ere we give an overview of the methods used forhe calculation of aerosol backscattering and extinc-ion coefficients, water vapor mixing ratio, and ofloud liquid water content, from the measured

ig. 6. Photon countings �no background subtracted� in the liquid2O channel �18000 laser shots per profile, 10-min average, 30-m

ange resolution�. The interference filters positioned in front ofhe channel are labeled �351-nm IF, �382-nm IF, and �403-nmF. The upper panel refers to a nighttime case for which a low-evel cumulus cloud was present; the bottom panel presents the

easurements in a clear atmosphere.

ayleigh–Mie and Raman-scattered signals. Fur- w

1

hermore, some estimation of the error is per-ormed. We place more emphasis on the techniquesed for the estimation of the liquid water contentithin low-level clouds, a procedure that is novelith respect to previous research �i.e., Refs. 2 and8�, because it takes advantage of the performancef our lidar receiver to discriminate between theaman-backscattered photons by H2O vapor and

iquid water.

. Aerosol Optical Parameters

ith regard to the measurements of the aerosol back-cattering and extinction coefficients, we should men-ion that the L’Aquila UV lidar, within theramework of a European project �European Aerosolesearch Lidar Network, �EARLINET�, Europeanommission �EC� funded�, which integrates a net-ork of aerosol lidars, has taken part in two inter-

omparison campaigns for testing and validating theardware setup and the retrieval algorithms.23–25

n the other hand, the Rayleigh–Mie and the Ramanidar inversion methods are well known,26,27 and itas been demonstrated that the combination of theifferent methods leads to an improvement of theesults. We refer to the cited papers23–25 for the de-cription of our algorithms and assessment of theata quality.

. Water Vapor

he standard expression of single-scattering �andegligible absorption by trace gases� Raman lidarignal can be written as follows:

�i �o��i�s� � �iiO�i�s� Po

�oTmol�o �s�Taer

�o �s�

� �d�Raman�i ��

d�ni�s��

4�Tmol

�i �s�Taer�i �s��s. (1)

n Eq. �1� P�i �o��i�s� is the number of photons �back-round subtracted� received at Raman-shifted wave-ength �i for the ith species �nitrogen, water vapor,nd liquid water� at excitation wavelength �o as aunction of range s; Po

�o is the number of photonsmitted by the laser at wavelength �o; �i

i is the totalfficiency �see Subsection 3.C� of the lidar Ramanhannel; O�i�s� is the overlap function of the outgoingaser beam and the Raman channel’s field of view;d�Raman

�i ��d�� is the Raman backscattering crossection of the ith molecule at excitation wavelengtho; ni�s� is the atmospheric molecular number densityf the ith species that performs Raman scattering;��1�s2� is the solid angle subtended by the Ramanhannel receiver; �s is the range resolution; Tmol

� �s�nd Taer

� �s� indicate the molecular Rayleigh and aero-ol Mie scattering transmission at wavelength �, re-pectively �note that the atmospheric transmissionsf the outgoing laser beam at wavelength �o differrom the transmissions of the returning signal at
avelength �i�; and these functions have the follow-

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ng main dependence from the atmospheric compo-ents:

Tmol� �s� � exp��

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s

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Taer� �s� � exp��

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s

�aer�s�, ��ds�� , (3)

here �mol� is the Rayleigh total cross section; nmol�s�

s the atmospheric molecular number density; andaer�s, �� is the aerosol extinction coefficient equal to0� dr�r2Qext�r, m, ��naer�r, s�. In this formulationhe optical depth between s1 and s2 is defined as �s1

s2

aer�s, ��ds. Qext�r, m, �� is the Mie extinction effi-iency of an aerosol of radius r and refractive index mnd naer�r, s� is the aerosol size distribution, numberensity of the aerosol with a radius between r and r �r.Taking the ratio between the Raman lidar signal

ssociated with the water vapor and the signal asso-iated with nitrogen, many terms in Eq. �1� cancel:

PH2 O�vap��s�

PN2�s��

�H2 O�vap�

H2 O�vap�

�N2

N2

OH2 O�vap��s�

ON2�s�

d�RamanH2 O�vap�

��

d�

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d�

�Tmol

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H2 O�vap��s�

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herefore, in a region in which the overlap functionspproach unity �in our system over the altitude rangebove 300 m�, the ratio between the Raman signals isroportional to the water vapor mixing ratio afterccounting for the differential optical transmission ofhe atmosphere.28

Since the estimation and�or the measurement ofhe first three factors in Eq. �4� is difficult, the usualxpression for the calculation of water vapor mixingatio �H2O

vap �s� �i.e., in grams of water vapor per kilo-rams of air� is

�H2 O

vap �s� � Cvap

TmolN2 �s�Taer

N2 �s�Tmol

H2 O�vap��s�Taer

H2 O�vap��s�

PH2 O�vap��s�

PN2�s�, (5)

here Cvap is a calibration constant29,30:

Cvap � K

d�RamanN2 ��

d�


��

d�

�H2

N2

�H2 O�vap�

H2 O�vap� , (6)

is a constant depending on the H2O and air molec-lar masses and the N2 volume mixing ratio. Thealibration constant Cvap can be evaluated by use ofhe water vapor sensor of standard radiosondes.he differential transmission factor �the second term

n Eq. �5�� can be determined by use of the ��4 de- w


endence of Rayleigh scattering by air molecules andssuming that the Raman measurement of the aero-ol extinction coefficient scales31 as ��1. The errorshat result from the statistical fluctuation of the lidarignals and those from the Cvap evaluation dominatehe indetermination budget.32

. Cloud Liquid Water

lthough in lidar sampling of water clouds the valid-ty of the single-scattering formulation of lidar equa-ions is questionable �we discuss this assumptionelow�, the cloud liquid water mixing ratio can, inrinciple, be obtained with an expression similar tohat in Eq. �5� by use of the ratio between the Ramanidar signal associated with liquid water and the sig-al associated with nitrogen:

�H2 Oliq �s� � Cliq

TmolN2 �s�Taer

N2 �s�Tmol

H2 O�liq��s�Taer

H2 O�liq��s�

PH2 O�liq��s�

PN2�s�.

(7)

n this formulation the calibration constant cannot bevaluated versus the measurement of liquid waterade with some other sensors. Constant Cliq in Eq.

7� is

Cliq � K

d�RamanN2 ��

d�

d�RamanH2 O�liq�

��

d�

�N2

N2

�H2 O�liq�

H2 O�liq� , (8)

nd it can be rewritten as

Cliq � Cvap


��

d�


��

d�

�H2 O�vap�

H2 O�vap�

�H2 O�liq�

H2 O�liq� , (9)

here Cvap is evaluated by use of balloonborne sen-ors. The ratio between the differential Ramanackscattering cross sections of vapor and liquidroplet H2O is a number between �1�10 and �1�0.2,18,19

Since it is possible to evaluate fll, the fraction of the

iquid water spectrum collected in the liquid waterhannel, and f�

�, the fraction of the water vapor spec-rum collected in the water vapor channel, we canrite

�H2 O�vap�

H2 O�vap�

�H2 O�liq�

H2 O�liq� ��H2 O�vap�

H2 O�vap�

�H2 O�liq�

H2 O�liq�

f��

fll . (10)

he ratio

�H2 O�vap�

H2 O�vap��H2 O�liq�

H2 O�liq�

these efficiencies do not take into account the Raman2O spectra, which are considered in f � can be di-

ectly estimated and�or measured by means of cali-rated light sources in a number of cases or setups ofhe lidar receiver. These measurements were made
ith a calibrated xenon light source L7810

�cnwet

tEscpTttl

ctactc

5

Ttcaualt

A

Ai

twpctacbdlcc

tg�owcwik

Ic

astWwtsFcvt

awlpwptS

defwwt

F1pcHd

Hamamatsu Photonics K.K.�, which has a slowhanging spectral irradiance between 300 and 450m. After the receiving telescope was illuminatedith the light source, the photon counts in the differ-

nt lidar channels were collected. The numbers ob-ained are affected by an error of less than 30%.

Estimation of the differential transmission func-ion term �the second factor on the right-hand side ofq. �7�� can be done as well as the water vapor mea-urements, but it could have minimal influence be-ause the wavelength scaling, namely, the Angstromarameter, of the cloud extinction is close to zero.his is particularly true2 in high optical depth condi-

ions associated with the presence of cloud particleshat are large with respect to the UV laser wave-ength.

The error that affects the final estimation of theloud liquid water content is calculated by propaga-ion in Eq. �7� of the error from the statistical fluctu-tions of the lidar signals and that of the calibrationonstant, which is determined mainly by experimen-al error of the Raman cross sections and of the lidarhannel spectral efficiencies.

. Example of Cloud Liquid Water Measurements

he following example refers to measurements duringhe night of 17 September 2001. A low-level cumulusloud developed between 1600 and 2000 m asl, duringpproximately 2 h of continuous observations. Fig-re 7 shows the lidar signals averaged over 10 min forperiod when the cloud was quite stable, i.e., the cloud

idar signals collected at 2-min intervals show varia-ions within the statistical fluctuation.

. Cloud Liquid Water Retrieval

ccording to the procedure described in Section 4, it

ig. 7. Measurements taken at night on 17 September 2001;0-min averaged lidar returns and 30-m range resolution. Thehoton counts were background subtracted: A, Rayleigh–Miehannel; B, N2 Raman channel; C, H2O vapor Raman channel; D,2O liquid channel. The error bars represent the �one standardeviation� statistical indetermination.

s possible to retrieve independently the aerosol ex- s

1

inction and backscatter coefficients as well as theater vapor and the cloud liquid water mixing ratiorofiles. For the latter, we provide a detailed dis-ussion of the procedure. The main point is the de-ermination of Cliq in Eq. �7�. According to Eqs. �9�nd �10�, we should know the water vapor calibrationonstant, the ratio between the differential Ramanackscattering cross sections of vapor and liquid�roplet H2O, and the ratio between the fraction of theiquid water spectrum collected in the liquid waterhannel and the fraction of water vapor spectrumollected in the water vapor channel.

In this particular session of measurements we ob-ained Cvap 35.7 � 1.8 �grams of water per kilo-ram of air�. We obtained this value by fittingusing the statistically weighted least-squares meth-d�, over a range of altitudes, the ratio between theater vapor and the nitrogen Raman lidar signals,

orrected for the differential transmission factor,ith the simultaneous radiosonde water vapor mix-

ng ratio measurements. According to currentnowledge �see Section 2�, we estimate that


��

d�


��

d�

� 0.062 � 0.015.

n addition, the channel efficiencies measured with aalibrated light source give

�H2 O�vap�

H2 O�vap��H2 O�liq�

H2 O�liq�� 0.17 � 0.05,

nd the convolution of the single channel relativepectral transmission with the Raman spectra of wa-er vapor and liquid water gives f�

��fll 1.12 � 0.15.

e obtained Cliq 0.42 � 0.17 �grams of cloud liquidater per kilograms of air�. The main indetermina-

ion in this calibration procedure concerns the inten-ity of Raman backscattering cross sections.inally, Fig. 8 shows the retrieved values for theloud liquid water along the measurements of waterapor mixing ratio and aerosol backscatter and ex-inction profiles.

The optical depth of the cloud is approximately 1.8,nd within the cloud the lidar ratio is below 20 sr,hich is typical of coarse droplets. The increase in

idar-derived water vapor in the cloud range is pro-ortional to the contribution of liquid water in theater vapor lidar channel, because a nonnegligibleart of the liquid water spectrum overlaps the spec-ral window of the water vapor lidar channel �seeubsection 3.C and Table 4�.We have also developed two procedures for an in-

irect validation of the cloud droplet liquid waterstimation. The first is based on the fact that araction of the liquid water signal is detected in theater vapor lidar channel and it assumes that,ithin the cloud, the water vapor is saturated over

he liquid droplet. Then the contribution to the lidar
ignal in the water vapor channel, within cloud range

sc

Hwmmpsl

w�cc

�

Bmro

rlci

opralspcT

penmfclltat�

am

liapw

rpsd

aew2w10attsdacuw

F2Cdptlitnlrr

6

c, that is due to the liquid water embedded in theloud droplets, can be estimated according to

�PH2 O�liq��sc� � PH2 O�vap�

�sc� ��H2 O

vap�sat�sc�

CvapPN2�sc�

�Tmol

H2 O�vap��sc�Taer

H2 O�vap��sc�

TmolN2 �sc�Taer

N2 �sc�. (11)

ence, �PH2Oliq

�sc� is the Raman backscattering in theater vapor channel in excess of 100% relative hu-idity, �H2O

vap�sat�sc� is the water vapor saturation massixing ratio, which is evaluated by simultaneous

ressure, temperature, and humidity �PTU� balloonounding. The ratio between �PH2O

�liq�

�sc� and theidar return in the liquid water channel PH2O

�liq�

�sc� is

�PH2 O�liq��sc�

PH2 O�liq��sc�

��H2 O�vap�

H2 O�liq�

�H2 O�liq�

H2 O�liq�

TmolH2 O�vap�

�sc�TaerH2 O�vap�

�sc�

TmolH2 O�liq�

�sc�TaerH2 O�liq�

�sc�, (12)

here the second factor on the right-hand side of Eq.12� is close to unity, and this ratio can be directlyompared with the ratio between lidar channel effi-iencies.

According to the optical setup of our lidar receiversee Subsection 3.C�,

�H2 O�vap�

H2 O�liq� ��H2 O�liq�

H2 O�liq� � 2.0.

y using Eqs. �11� and �12� with the lidar measure-ents of 17 September 2001, we obtained a cloud

ange of �PH2O�liq�

�sc��PH2O�liq�

�sc� � 2.0 � 0.5. In spite

ig. 8. Measurements �10-min averaged� taken on 17 September001. A, � cloud backscatter profile; B, � cloud extinction profile;, lidar ratio �LR� �� profile; D, below the cloud range, lidar-erived water vapor �WV� mixing ratio profile �black line� com-ared with the local PTU balloon sounding �dashed line�. Withinhe cloud range, the water saturation mixing ratio profile �dashedine� is also shown. It should be noted that, in the cloud range, thencrease of lidar-derived WV �shown in the figure� is proportionalo the contribution of the liquid water �LW� in the WV lidar chan-el, which must be considered as a bias to the real WV profile. E,

idar-derived LW mixing ratio profiles �see text�. The error barsepresent the standard deviation �statistical and systematic er-ors� but not for the WV profile in the cloud range.

f the different assumptions and estimations, this t


esult is quite encouraging. We also obtained simi-ar agreements or indirect checks in almost all theases in which we measured the cloud liquid contentn cumulus clouds.

Another procedure that can be considered as anff-line check is based on evidence obtained in thelanetary boundary layer �PBL�, i.e., the closest lidarange. In a clear-sky condition or over a range ofltitudes free of clouds, we measured a signal in theiquid water channel. Extensive laboratory testshowed that this channel strongly rejects out-of-bandhotons, which leads to the conclusion that we areollecting photons at a wavelength close to 393 nm.his could be due to

�a� Raman backscattering of the liquid waterresent in the PBL hydrated aerosols. Veselovskiit al.33 claim that in clear conditions the Raman sig-al from liquid water inside the PBL is approxi-ately 1 order of magnitude lower than the signal

rom water vapor. This particular point of view isorroborated by the observations of Krieger et al.34 inaboratory experiments on a single H2SO4�H2O drop-et. They observed that a common feature of con-aminated �i.e., exposed to laboratory air� droplets isstrong fluorescence background superimposed upon

he Raman spectrum in the region of OH stretching3000–3600 cm�1�.

�b� Fluorescence induced in the optical fiber or innother part of the receiver by the lidar return,ainly the elastic backscatter �i.e., Sherlock et al.35�.�c� Laser-induced fluorescence of atmospheric mo-

ecular N2; although it is expected that the fraction ofonized nitrogen molecules is very low, the first neg-tive band of N2

� has its maximum intensity at ap-roximately 3914 Å, i.e., quite close to the centralavelength of the liquid water lidar channel.

The setup and the spectral responses of our lidareceiver do not help in the determination of whichrevious hypothesis is valid, but, with a critical in-pection of the lidar signals, we can estimate theetection limit of the liquid water retrieval.In particular, if we accept hypothesis �a�, we can

dopt, for a first guess, the calibration used for thestimation of the cloud liquid water to determine theater content in the PBL. From the 17 September001 measurements we determined that the liquidater content in the PBL hydrated aerosols �between000- and 1600-m altitude range� was approximately.005 � 0.003 �grams of liquid water per kilogram ofir�. Since, in a range of altitudes, it is possible forhe presence of a fluorescent background, we expecthat the ratio between the differential Raman back-cattering cross sections of vapor and the liquid–roplet H2O can strongly differ with respect to thatssumed for the cloud liquid water estimation; itould be underestimated. Hence the previous eval-ation can be considered a kind of lower limit of liquidater content in the PBL.On the other hand, if the measured signal is due to

he fluorescence process outlined in �b�, we expect

ttRm1rSccaotlaqcmwptpnswp

slamSrs

tcioikim

B

Wmsmsaooca

r

ac

wdasci

AiMdoisca

wdttlmtat

A1Ftdd

hat, in the closest lidar range �range of altitudes sd�,he ratio between the liquid water signal and theayleigh–Mie signal is nearly constant. For theeasurements shown in Fig. 7 �between 1000 and

600 m�, this assumption seems reasonable and thisatio is constant to within 30% �standard deviation�.imilar behavior can be found in most of the otherloud measurements. Assuming that this fluores-ence process is localized in the optical fiber, the rel-tive efficiency of the fluorescence itself can bebtained by the ratio between the liquid water andhe Rayleigh–Mie signals weighted for the relativeidar channel transmissions �see Table 4�, we obtain

fluorescence efficiency of �10�6. This estimate isualitative and we can only state that such a fluores-ence contribution constitutes a small bias to theeasurement of the liquid water content as well as ofater vapor. In such a situation, the fluorescencerocesses in the optical fiber additionally contributeo all the Raman lidar returns. Since the water va-or and the cloud liquid water are estimated begin-ing with the ratio between the different Ramanignals, this systematic bias is partially damped, ande estimate that it is less than 0.001 �grams of waterer kilogram of air�.We believe that hypothesis �c� is quite unrealistic,

ince the spectral features eventually detected in theiquid water lidar channel require that a fraction oftmospheric N2 should be ionized. In addition, inany of our measurements, as well as for the 17eptember 2001 session, we cannot claim that theatio between the liquid water signal and the N2ignal is strictly constant.Finally, we believe that it is reasonable to assume

hat the lidar return collected in the liquid waterhannel from the PBL is due to the water embeddedn the aerosol droplets. To be realistic we considerur estimate of the lower limit of liquid water contentn the PBL, i.e., �0.005 �grams of liquid water perilogram of air�, as the sensitivity limit of our exper-

mental setup and of the retrieval procedure for esti-ating the cloud liquid water content.

. Estimation of Cloud Droplet Size Distribution

e can delve further into the data analysis to esti-ate some parameters related to the cloud droplet

ize distribution. Whiteman and Melfi2 outlined theain points of this retrieval technique that uses Mie

cattering theory and makes some assumptionsbout the composition of cloud droplets and the shapef their size distribution. But, since we are focusedn the performance of our system in detecting theloud liquid water, we follow a more conservativepproach.The extinction coefficient, measured in the cloud

ange, is �see the details following Eq. �3��

�aer�sc, ��

dr�r2Qext�r, m, ��naer�r, sc�, (13)
�0 d
1

nd the volumetric cloud liquid water content �LWC�an be written as

LWC�sc� � �H2 Oliq �sc��air�sc�

� �0

� 43

�r3�w naer�r, sc�dr, (14)

here naer�r, sc�dr is the number density of cloudroplets in the radius range �r, r � dr�, �w and �air�sc�re the water and air volumetric mass densities, re-pectively. Furthermore, the ratio between theloud liquid water content and the aerosol extinctions

LWC�sc�

�aer�sc, ��

43

�w

�0

�

drr3naer�r, sc�

�0

�

drr2Qext�r, m, ��naer�r, sc�

.

(15)

t the specific wavelength of � 351 nm, a refractivendex of water of m 1.33007,36 and calculating the

ie scattering extinction efficiency by use of stan-ard routines,37,38 it appears that Qext�r, m, �� is anscillating function of r that asymptotes to 2 withncreasing r. For UV light, oscillations becomemall for r � 1 m. Thus, for warm water clouds wean assume that Qext�r, m, �� 2. Hence, at anyltitude within the cloud range, we can calculate

reff�sc� �3

2�w

LWC�sc�

�aer�sc, ��, (16)

here reff�sc� is the mean effective radius of the cloudroplet size distribution defined as the ratio betweenhe third and the second moments of the size spec-rum.39 The effective number concentration of drop-ets Neff�sc� is defined as the concentration of the

onodisperse size distribution having the same wa-er content LWC�sc�, extinction coefficient �aer�sc, ��,nd effective radius reff�sc� as the droplet size spec-rum naer�r, sc�.

Neff�sc� can be expressed as

Neff�sc� �

��0

�

drr2naer�r, sc��3

��0

�

drr3naer�r, sc��2 �2�w

2

�

��aer�sc, ��3

�LWC�sc��2 .

(17)

pplying Eqs. �16� and �17� for the cloud measured on7 September 2001, we obtain the data reported inig. 9. The effective radius of the droplet distribu-ion is between �15 and �80 m, and the effectiveroplet concentration ranges between �0.1 and �1roplets�cm�3.As a marginal comment, it should be noted that the

roplet effective radii are smaller at the bottom of the


cdcpcebdaaila

rspriosndtratapmtctRmtc

lptasr

6

Tseiatll

s

u

ti

ttlbbutc

i

Fwut

F2ditl

6

loud than above. This behavior is typical of waterroplets that grow in convective clouds, but it is alsoonsistent with the increase in size distribution dis-ersion40 when ascending in the cloud layer. Thisan be caused by the mixing between the cloud and itsnvironment at the growing cloud top.41 The PTUalloon sounding, taken simultaneously with the li-ar sampling, indicates that this cloud was formed inn unstable environment, and the potential temper-ture lapse rate profile suggests that, above 1850 m,t would be expected that the updraft and the turbu-ent mixing between the cloud and its environmentre quite efficient.For this case study the retrieved cloud effective

adii and effective droplet densities are larger andmaller, respectively, than the estimates reported inapers that summarize a large amount of data withegard to the microphysical properties of clouds fromn situ42 and�or satellite measurements.43 On thether hand, if we assume that the cloud droplet sizepectrum is well described by a monomodal log-ormal distribution40 with a large geometric stan-ard deviation �i.e., � � 3, which means that �70% ofhe total number of droplets is between r0�� and �

0�, the mode radius ranges between 0.5 and 5 m,nd the cloud droplet number density ranges be-ween 10 and 100 cm�3. These values appear togree with the typical variability of the microphysicalarameters of warm clouds.44–46 Finally, we mustention that, in addition to the different assump-

ions �e.g., Qext�r, m, �� 2�, the above estimatesould be influenced by our retrieval of the cloud ex-inction although most of the quantities derived fromaman lidar data �i.e., water vapor and liquid waterixing ratio� are not influenced by the multiple scat-

ering but are based on ratios of lidar signals.47 The

ig. 9. Measurements �10-min averaged� taken on 17 September001. A, effective cloud droplet mean radii; B, effective cloudroplet number densities. We calculated the errors by propagat-ng the indetermination that affects the measured cloud LW con-ent and extinction �see text for the discussion with regard to theimitations of these estimates�.

loud extinction calculated by use of only a single t


idar signal can be significantly influenced by multi-le scattering. In particular, the apparent attenua-ion of the propagating laser beam decreases, causingn underestimate of the extinction, resulting in aystematic overestimate of the effective cloud dropletadii.

. Conclusions and Perspectives

he setup of our Raman lidar allows reliable mea-urements of tropospheric aerosol backscattering andxtinction coefficients, water vapor mixing ratio, and,n addition, it discriminates between the water vapornd the cloud liquid water Raman-backscattered pho-ons. We have shown that an estimate of the cloudiquid water content is possible when sampling lowevel clouds if

the lidar channel spectral efficiencies can be mea-ured and�or estimated,the water vapor lidar calibration constant is eval-

ated, andthe ratio between the differential Raman backscat-

ering cross sections of vapor and liquid�droplet H2Os known.

Indirect validations of the cloud liquid water re-rieval can be performed by use of the marginal crossalk between the water vapor and the liquid wateridar channels, and knowing the degree of overlapetween the water vapor and the liquid water Ramanackscattering spectra. The performance of the liq-id water Raman channel in detecting a backscat-ered signal, in clear-sky conditions, could beompatible with

Raman backscattering of the liquid water presentn PBL hydrated aerosols and�or

fluorescence induced by the lidar return in the op-

ig. 10. Lidar-derived LW mixing ratio profiles for a selection ofarm liquid cloud observations. The profiles were obtained byse of 10-min averaged lidar signals. The error bars representhe standard deviation �statistical and systematic errors�.

ical fiber or in another part of the receiver.

sllfwotts0a

sidctutcmctTcdmsacbtmtvtdc

bbsbt�

bsr

is

suoout�ssvce

vcstmw

R

1

1

These hypotheses have been used to assess theensitivity limit of our experimental setup and of theiquid water retrieval procedure. We have selectedidar observations of clouds whose tops never reachreezing temperatures �warm clouds�. The liquidater content measured in a relatively stable period

f the clouds is shown in Fig. 10. In the cold monthshe liquid water content maximum, usually close tohe top of the cloud, is slightly lower than duringpring and summer observations, 0.4 � 0.2 g�kg and.5 � 0.3 g�kg, respectively. These values appear togree with other reported measurements.2,43,45

Although the Raman lidar technique for the mea-urement of aerosol and water vapor is still evolv-ng,48,49 for the purpose of cloud liquid wateretection the main problems are the calibration pro-edure and the estimate of water Raman cross sec-ions. A plan should be formulated to find a betterse of external calibrated sources, i.e., on-line rela-ive calibration of the Raman channels. Keeping aonservative approach and using the simultaneouseasurements of cloud extinction and liquid water

ontent, we have attempted to retrieve the main fea-ures of the cloud water droplet size distribution.he results show that we have overestimated theloud droplet mean radii and underestimated theroplet number densities, which we expect is due toultiple scattering that occurs in a cloud. Multiple

cattering is much more likely when large particlesre encountered because the forward scattering in-reases. This forward-scattered component is addedack into the propagating laser beam and decreaseshe apparent attenuation of the beam itself. Thus,ultiple scattering decreases the cloud droplet ex-

inction measured by lidar compared with its actualalue. In addition, some parameters of the lidar sys-em, such as the telescope field of view and laserivergence, also influence the multiple scatteringomponent of the signal.49,50

The quantities derived from Raman lidar data andased on ratios of lidar signals �i.e., water vapor andackscatter coefficient� are not influenced by multiplecattering.47 In principle, we could use the cloudackscatter coefficient and the cloud liquid water con-ent to estimate cloud droplet properties. Equation15� can be rewritten as

LWC�sc�

�aer�sc, ��

43

�w

�0

�

drr3naer�r, sc�

�0

�

drr2Qback�r, m, ��naer�r, sc�

,

(18)

ut the Mie backscatter efficiency, Qback�r, m, ��, is atrongly oscillating function of the radius, and noeasonable assumptions can be done to approximate

�

drr2Qback�r, m, ��naer�r, sc�
�0 1
1

n a form close to the second moment of the sizepectrum.If we were to assume a three-parameter log-normal

ize distribution, it would be possible to retrieve val-es of the median radius and geometric dispersion byther methods, such as a least-squares method, or byther more advanced techniques such as hybrid reg-larization,51 neural networks,52 or maximum ex-ropy regularization.53 But such algorithmsnonlinear ill-posed inversions� are sensitive to mea-urement errors.51–53 The future development ofuch a Raman technique would be to implement aersion of the Raman lidar equations that would in-lude a parameterization of the multiple scatteringffects.48,50

This research has been partially funded by the En-ironment Program of the European Union underontract EVR1-CT1999-40003 �European Aerosol Re-earch Lidar Network� and by CETEMPS �Integra-ion of remote sensing techniques and numericalodeling for the forecast of severe weather; http:��ww.aquila.infn.it�CETEMPS�.

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1

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wrt

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aer�r, sc� �

�N�sc��2� r ln��sc��exp��1⁄2ln2�r�r0�sc��ln2��sc� ,

here N�sc� is the droplet total concentration, r0�sc� is the modeadius, and ln��sc� is the geometric standard deviation. The effec-ive radius is related to r0�sc� and ln��sc� according to

reff�sc� � r0�sc�exp�5 ln2��sc��2 .

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4

4

4

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1

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raman lidar observations of cloud liquid water

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