Lidar retrievals of cloud droplet number concentration at the cumulus base: A feasibility study

Lidar retrievals of cloud droplet number concentration at the cumulus base: A feasibility study

    Lidar Retrievals Of Cloud Droplet Number Concentration At The Cumulus Base: A Feasibility Study T. Stacewicz, M. Posyniak, S. Sitarek...

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    Lidar Retrievals Of Cloud Droplet Number Concentration At The Cumulus Base: A Feasibility Study T. Stacewicz, M. Posyniak, S. Sitarek, S.P. Malinowski PII: DOI: Reference:

S0169-8095(13)00305-0 doi: 10.1016/j.atmosres.2013.10.023 ATMOS 3008

To appear in:

Atmospheric Research

Received date: Revised date: Accepted date:

28 February 2013 28 October 2013 29 October 2013

Please cite this article as: Stacewicz, T., Posyniak, M., Sitarek, S., Malinowski, S.P., Lidar Retrievals Of Cloud Droplet Number Concentration At The Cumulus Base: A Feasibility Study, Atmospheric Research (2013), doi: 10.1016/j.atmosres.2013.10.023

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ACCEPTED MANUSCRIPT LIDAR RETRIEVALS OF CLOUD DROPLET NUMBER CONCENTRATION AT THE CUMULUS BASE: A FEASIBILITY STUDY

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Institute of Experimental Physics, Faculty of Physics, University of Warsaw, ul. Hoża 69, 00-681 Warsaw, Poland [email protected] Institute of Geophysics, Faculty of Physics, University of Warsaw, ul. Pasteura 7, 02-093 Warsaw, Poland [email protected] 3

Institute of Geophysics, Polish Academy of Sciences ul. Księcia Janusza 64, 01-452 Warsaw, Poland [email protected],

Institute of Applied Optics, ul. Kamionkowska 18. 03-805 Warsaw, Poland [email protected]

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T. Stacewicz1, M. Posyniak2,3, S. Sitarek4, S.P. Malinowski2

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ABSTRACT

The properties of atmospheric aerosol under a cumulus base were studied using three-

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wavelength lidar. A growth of hygroscopic aerosol particles in a convective updraft and the activation of cloud condensation nuclei (CCN) were observed. A simple and robust model of droplet formation in a rising parcel was used as a closing assumption to the original approach of cloud droplet number concentration (CDNC) retrieval. The potential to retrieve the vertical profile of the effective radius of droplets near the cloud base and the height of activation and condensation of nuclei is demonstrated.

KEYWORDS: lidar, cloud droplet number concentration, cumulus base, remote sensing

ACCEPTED MANUSCRIPT 1. INTRODUCTION

The cloud droplet number concentration (CDNC) is a key microphysical parameter used in

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estimates of radiative properties of clouds in climate and weather models. Under the given

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thermodynamic conditions for a given type of clouds, the CDNC depends on the details of the condensation process. In particular, the size distribution and hygroscopicity of atmospheric aerosols and the rate of supersaturation production related to the vertical velocity at the cloud

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base are important (for example, see the classic paper by Twomey, 1959, or a recent study by Partridge et al., 2011). These local properties and processes cannot be directly included in

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large-scale weather and climate models. Adequate parameterizations are necessary (see, e.g., Mc Figgans et al., 2006, Tao et al., 2012).

The development of affordable remote sensing procedures aimed at the validation of such parameterizations and monitoring of microphysical and radiative properties of clouds is desirable. Feingold et al. (1998) have discussed the feasibility of multisensor (active - lidar

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and radar, passive – radiometers) retrievals of cloud microphysical properties. Many studies propose and test particular combinations of remote sensing techniques, which are occasionally

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supported by additional in-situ measurements (see, e.g., Boers et al., 2000, Ghan et al., 2006, Martucci and O'Dowd, 2012).

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In this paper, we propose a different, simpler and more specific approach to the problem of CDNC estimation with the use of a multiwavelength lidar directed vertically at the cloud base.

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Feingold and Grund (1994) have studied the theoretical feasibility of a similar approach nearly 20 years ago. Feingold and Grund concluded that a combination of UV, visible and far infrared beams in the lidar system is necessary to perform successful retrievals. Instead, we apply a standard, three-wavelength (1064 nm – near infrared, 532 nm - visible and 355 nm – near UV) aerosol lidar and a specific modification of the aerosol particle size distribution (APSD) retrieval technique by Jagodnicka et al. (2009a). The modification includes the use of atmospheric sounding data supported by physically based information on the activation of cloud condensation nuclei (CCN) derived from a bin model of droplet growth in an adiabatic rising parcel (Arabas and Pawlowska 2011). A variety of parcel models, preceded by Twomey (1959), are currently widely adopted in the numerical modeling of convective processes (e.g., Khvorostyanov and Curry, 1999; Celani et al., 2008) and in elucidations of in-situ measurements (e.g., Colón-Robles et al., 2006). The model we select (Arabas and Pawlowska 2011) is a readily available tool, optimized to

ACCEPTED MANUSCRIPT accurately represent the finest details of particle size spectrum evolution. We organize the present paper in the following manner. In the next section, basic information on the employed lidar system and on the atmospheric conditions over the course of the

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feasibility study is provided. Collected lidar profiles from the cloud base region are presented.

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The results of parcel model calculations are described in section 3. The principle of the APSD retrieval technique is presented in section 4, then constraints from the parcel calculations are applied to the retrieval procedure. Finally, in section 5, the results of the retrievals are

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presented and discussed.

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2. INSTRUMENTATION AND MEASUREMENTS

The details of the lidar construction that was used can be found in Jagodnicka et al., 2009a and Jagodnicka et al. 2009b. Briefly, the pulsed Nd:YAG laser is used in the optical transmitter. This laser generates beams at wavelengths of 1064, 532 and 355 nm. The energy

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of the light pulses reach 100 mJ, the full width at half-maximum duration time is approximately 6 ns and the repetition rate is 10 Hz. In the optical receiver, a Newtonian

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telescope with a 400 mm diameter mirror with a focal length of 1200 mm is used. The return light pulses collected by the telescope are spectrally separated by a polychromator and

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registered in the channels corresponding to the consecutive wavelengths. The signals from the photomultipliers installed in each channel are digitized by 12-bit A/D converters. The lidar

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overlap reaches approximately the altitude z0 ≈ 1 km (Stelmaszczyk et al., 2005). The FOV of the telescope is approximately 1 mrad. During the acquisition of measurements, the lidar profiles were averaged over 150 pulses. Therefore, the temporal resolution of 15 s was achieved.

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a)

b)

Fig. 1. a) MODIS image from 30. 07.2008 10.00 UTC showing the investigated clouds. Black arrows indicate the locations of the aerological sounding (upper arrow) and the lidar. b)

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Typical view of the sky over the course of the measurements (a photograph facing ENE taken at 10:23 UTC ).

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Lidar data were collected in Warsaw on 30 07.2008at 11-13 local time (09-11 UTC). On this day, fair weather cumuli were developing in a mass of marine polar air advecting from the northeast in the peripheries of the Scandinavian high-pressure system. Fig. 1 presents the

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MODIS visible image from 10.00 UTC, accompanied by a view of the sky from the observation location. Atmospheric sounding from 12 UTC (a balloon was launched at

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approximately 11.15 UTC in nearby WMO 12374 Legionowo) shows a well-mixed boundary layer extending up to 1660 m, and a sheared cloud layer above the boundary layer extending to 2130 m and capped by a 130 m deep inversion of 2K.

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Fig. 2. a) Signatures of cumulus clouds on the whole series of lidar signals b) an expanded portion, presenting details of consecutive profiles. Arrows point to the profiles classified as a

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“cloud base”. The lidar signal amplitude is presented in a gray scale in arbitrary units.

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The laser beams, projected vertically, are pointed at shallow cumulus clouds, tilted by the wind shear, drifting slowly (2 - 4 m/s) above the lidar station. The profiles, averaged over

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15 s, correspond to the horizontal averaging of the returns over the distances of 30-60 m. Fig. 2a presents the time series of all of the 480 collected profiles arranged in a map. Laser light penetrated the clouds only within the depth of 30 - 50 m (Wandinger, 1998). Therefore, only the signature of the lower layers of the cloud is presented in the picture. An expanded segment of the series showing the variability of the signals is presented in Fig. 2b. The arrows indicate profiles classified as uniform adiabatic updrafts at the cloud base (referred to later as the “cloud base”), suitable for application to the retrieval algorithm. These profiles fulfilled the following criteria: 1) location inside the cloud signature (not at the cloud edge); 2) presence of a single and well defined maximum of the lidar signal; 3) the lowest positions of the signal maximum. The first two conditions allowed the rejection of profiles recorded in varying conditions within a 15 s averaging period; the last condition was used to reject entraining parcels. The

ACCEPTED MANUSCRIPT conditions were conservative; thus, only 12 profiles from the measurement series met these criteria. Another group of 53 profiles with a cloud signature and a single maximum of the lidar signal were classified as “cloud side”. The retrieval procedure, described later, was

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applied to both groups of profiles to investigate the differences between the group most likely

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fulfilling the assumptions used in the retrieval procedure (“cloud base”) and the others (“cloud side”).

During the course of the analyzed period, the cloud base height increased from approximately

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1400 m at 09.00 UTC to nearly 1700 m at 11.00 UTC. This range of cloud base and the heights and the altitude range of increased returns from the cloud sides agree with the

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atmospheric sounding.

3. PARCEL MODEL CALCULATIONS

The profiles of the temperature and humidity from the atmospheric sounding were used in

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parcel model calculations of the evolution of particle size spectra at the cloud base. We used adaptive bin calculations with the code of Arabas and Pawlowska (2011), which uses the κ-

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Koehler approach (Petters and Kreidenweis, 2007). Aerosol evolution in the updraft at the cloud base was calculated using the thermodynamic properties of air in the mixed layer.

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Constant updraft velocities in a range from 0.5 m/s to 4.0 m/s (see, e.g., Doppler lidar observations by Ansmann et al., 2010) and two values of κ = 0.04 (corresponding to a non-

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hygroscopic aerosol) and κ = 0.64 (corresponding to a highly hygroscopic aerosol) (Petters and Kredenweis, 2007) were selected to cover a wide range of possible physical and aerosol conditions. Initial aerosol size distributions, in the form of a two-mode lognormal function (described later), were obtained from the APSD estimates at the altitudes below the cloud activation height zA (described later). From this level, parcel model runs were performed approximately 300 m down and 200 m up, covering a 500 m deep region. The example results, shown in Fig. 3, indicate that to the first approximation, the number of the activated particles (the number of particles with a radius greater than 100 nm at a height indicated as zC) increase with the updraft velocity. However, the depth of the activation zone (the zone of rapid increase of the number of particles with a radius greater than 100 nm) depends on aerosol hygroscopity.

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Fig. 3. Number of particles of radius greater than 100 nm as a function of the relative altitude

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for various lift speeds v [m/s] and the hygroscopity coefficient κ. The activation level zA and the condensation level zC are shown for κ=0.04.

The following conclusions were drawn from the results of these simulations: The activation concerns only the particles with a radius exceeding a specific

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boundary value rmin at activation level zA (c.f. Fig. 4 in Mc Figgans et al., 2006 or Fig. 2 of Arabas and Pawlowska, 2011). Both parameters are determined by the

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model. In the range of the investigated updraft velocities (0.5 < v < 4 m/s) and for both values of the hygroscopity parameter, the value of the boundary radius was

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found to be rmin = 100 ± 20 nm. Note that rmin exceeds the typical critical dry sizes for cloud droplet activation (e.g., a range of 25-75 nm in the review paper of Mc

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Figgans et al., 2006) but refers to the diameter at the activation level zA. Thus, CDNC can be estimated from the integration of the right-hand side of the APSD function n(r) at the activation level zA as given in the following equation: ∞

CDNC= ∫ n(r )dr r min

ii)

(1)

Starting from the activation altitude zA, the activated droplets constitute a new Gaussian mode of APSD. The amplitude of this mode increases with the height due to the growing number of activated droplets. A median radius of the mode r0 and its width σ remain constant: r0 ≈ 1000 nm, σ ≈ 500 nm.

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For the particles of radii smaller than rmin, the APSD remains unchanged.

iv) At the specific condensation altitude zc, all of the hygroscopic particles of the radii r > rmin at zA become activated. Further growth (for z > zc) of the size of the

ACCEPTED MANUSCRIPT activated droplets occurs due to the condensation. This growth can be expressed by an increase of the median radius of the Gaussian mode of APSD, whereas its amplitude and width remain constant (c.f. Figs 3 and 7 in Arabas and Pawlowska,

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2011).

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4. LIDAR SIGNALS AND THEIR ANALYSIS

Fig. 4 presents an example of range-corrected lidar profiles (with a 9 m vertical resolution) near the altitude range classified as a the cloud base. A value of zero was set at the

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condensation altitude (zc), which is explained in section 4.1. In general, the presented profiles are typical for the lidar signals at the cloud base, as reported, for example, in Apituley et al.,

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(2000) and Boers et al., (2000).

Fig. 4. An example of range-corrected lidar signals in the vicinity of the cumulus cloud base. zA and zc denote the activation and the condensation altitudes, respectively.

At the altitudes below –30 m, the returns are weak, similar to those in the boundary layer below. This result suggests that the light is scattered by non-activated aerosol particles. According to the results of simulations with the parcel model of Arabas and Pawlowska (2011), the size distribution of the non-activated aerosol particles spans from approximately 10 nm to 200 nm with the maximum of approximately 80 nm. For these altitudes, the technique of APSD retrieval, described in (Jagodnicka et al., 2009a) and shortly presented in the next section, was applied in its generic form.

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4.1. RETRIEVALS BELOW ZA

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A predefined form of the APSD function with several free parameters is assumed. For our

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three-wavelength lidar, we use a bimodal combination of lognormal functions. An additional assumption is that aerosol consists of spheres of known refractive index (Shifrin and Zolotov,

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1997) or (Ligon et al., 2000). The sphericity is justified for the hygroscopic aerosol at a high relative humidity close to the cloud base. The sensitivity to the value of the refractive index was checked in a series of numerical tests, and we found that the uncertainty is less than the

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other uncertainties in the retrieval procedure (see the Results section). Using the predefined form of APSD and the Mie approach (Bohren and Huffman, 1999), we calculate the backscattering coefficient and the total scattering coefficients according to the following expressions:

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β λ ( z)=∫ πr2 Q βλ ( r)n(r,z )dr

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α λ ( z)=∫ πr 2 Qαλ (r )n( r,z)dr

, (2)

for each wavelength λ in a range of distances z < zA, starting from the lidar overlap altitude z0.

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Here, Qαλ(r) and Qβλ(r) are total scattering and backscattering coefficients, respectively. After substitution of the obtained coefficient into a set of range-corrected lidar equations, we can

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express the following equation:

[

z

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L λ ( z )=A λ β λ ( z )exp −2 ∫ α λ ( x )dx z0

]

,

(3)

in which the calculated signals expressed by the right side of (3) are compared with the measured signals (Lλ(z)). Application of the minimization procedure (see Jagodnicka et al., 2009a for details) allows the acquisition of the optimal parameters characterizing n(r,z), the predefined (two-mode log-normal) APSD. Direct substitution of the extinction and backscattering coefficients into (3) ensures that the APSD remains as the only unknown function in the system of equations. The method does not require knowledge of the lidar ratio. At the altitudes marked as zA (the lower arrow in Fig. 4), a systematic increase in the mean values of lidar signals is observed. This result is considered a signature of the beginning of CCN activation and growth into cloud droplets. Therefore, we assume that this level corresponds to the appearance of the new Gaussian mode of droplet size distribution. At zA,

ACCEPTED MANUSCRIPT we change the algorithm of the APSD retrieval using additional information from the model of CCN activation in the adiabatic parcel; details are described in the next section. Close to the signal maximum, lidar returns are strongly affected by multiple light

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scattering, which might cause an error as high as 50 % (Wandinger, 1998). Consequently, the

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signals above the maximum are not analyzed.

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4.2. RETRIEVAL ALGORITHM FROM ZA TO ZC

Based on the above assumptions and conclusions from the parcel model, we modify a

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predefined APSD function. This is accomplished in the following steps: We set zA as the altitude at which the activation process begins. Consequently, a systematic increase in the mean value of lidar signals should be observed above this altitude. According to the results of the parcel model (Arabas and Pawlowska, 2011, sections 4.1, 2 and 3) at this level, the APSD is divided into two parts: for r < rmin, the APSD persists in its initial form, as it was determined for z < zA (see section. 4.1),

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whereas for r ≥ rmin, a Gaussian mode containing NA(z) particles is generated. Then, the backscattering and total scattering coefficients (βλ(z) and αλ(z) (see eq. 2) are

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calculated. Using the formula (3), the range-corrected lidar signals Lλ(z) are found and compared with the measured signals, using the minimization procedure The

mode.

Because the determination of zA is ambiguous, the procedure is repeated starting with

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ii.

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result provides the opportunity to determine spatial changes of NA(z) of the Gaussian

the neighboring altitudes (zA ± 9 m, ± 18 m etc.). The final caesura of the zA level evaluation is the consistency of the increase of the Gaussian mode amplitude with the altitude.

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Fig. 5. Changes of aerosol particle size distribution with altitude starting from the

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activation altitude zA and consecutive altitudes to the condensation altitude zc and above.

After this iteration, the activation altitude is finally determined. The following evolution of the modeled APSD within the activation range zA < z < zc is shown in

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Fig. 5. The condensation altitude zc (marked also in Fig. 3 and Fig. 4) is reached when all of the droplets of r ≥ rmin are activated. This altitude corresponds to the

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relation: NA(zc) = CDNC.

iii) With regards to the results of the parcel model (section 3, iv) above the condensation

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altitude zc, the increase of the lidar signals (Fig. 4) occurs due to the condensational growth of the activated droplets. This increase is reflected by the increasing median

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radius r0 of the Gaussian portion of the APSD at the constant number concentration CDNC. The APSD function continues to be unchangeable in its initial form for r < rmin. A comparison of the synthetic lidar signal (calculated using this assumption) with the measured signal provides an opportunity to determine r0 for each altitude. Within these consecutive steps, the APSD function n(r,z) for each observed altitude can be determined (Fig. 5) and used, for example, to calculate the effective radius of the droplets expressed in the following equation (see Hansen and Travis, 1974):

r 3 n(r,z )dr ∫ r eff ( z )= 2 ∫ r n( r,z)dr

(4)

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4.3. SYNTHERIC AND MEASURED LIDAR PROFILES

Fig. 6. A comparison of the measured and synthetic lidar signals; open circles represent registered signals; triangles represent synthetic signals.

ACCEPTED MANUSCRIPT Finally, to check the feasibility of our approach, the artificial lidar signals were synthesized using the APSD functions from Fig. 5 and compared with the measured signals (Fig. 4). The example results for all three wavelengths are shown in Fig. 6. Because an agreement between

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the measured and the synthetic signals is typically better than (50 %) error of our

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measurements (see Jagodnicka 2009a), the comparison confirms the consistency of the APSD retrieval procedure.

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5. RESULTS AND DISCUSSION

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We applied the retrieval procedure to all of the profiles classified as “cloud base” and “cloud side” but calculated separate retrieval statistics to visualize the differences between the cases in which the criteria for the adiabatic parcel are most likely fulfilled along with the other

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cases. Figs. 7 and 8 present these statistics.

Fig. 7. Number of activated droplets NA(z) as a function of the relative altitude (zc= 0) retrieved for profiles classified as “cloud base” (a) and “cloud side” (b).

In this preliminary study, the initial APSD is determined with a precision of 50 % (Jagodnicka at. all 2009a) and the rmin with a precision of 20 %. In effect, the droplet number concentration is estimated as CDNC = 2400 ± 1500 cm-3. Such high values of CDNC are possible in polluted urban areas; for example, Conant et al., 2004 have reported CDNC = 2300 in warm cumuli developed in a polluted air mass. The standard deviation of the CDNC estimates from the profiles classified as a “cloud base” lies within the range of the conservative estimate of the error of the method.

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Fig. 8. The effective radius as a function of relative altitude (zc=0) in profiles classified as “cloud base” (a) and “cloud side” (b).

The “cloud base” class is characterized by a smaller spread of estimated values of

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CDNC and by the effective radius compared with the “cloud side” class. This result suggests that the additional information from the model is important for the retrieval procedure. The decrease of NA and the fluctuations of reff at the topmost end profiles can affect the

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low-number statistics (only a few shots reach this level). Alternatively, the decrease of NA and the fluctuations of reff are an artifact due to secondary scattering, increasing with the deeper

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penetration of lidar light into the cloud. Fig. 6 shows indirect confirmation of the latter argument in which synthetic lidar signals, not accounting for secondary scattering, deflect

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from the observed signals. Regardless of the explanation, the two topmost points from the profiles should be rejected. The parcel model simulations (Fig. 3) clearly reflect that for a given aerosol size distribution below the activation level, the number of activated droplets (and, subsequently, cloud droplets) depends on the updraft velocity. A comparison of cloud droplet number concentrations in Figs. 3 and 7a suggests that in the observed clouds, the most probable updraft velocity at the cloud base is ~2 m/s. Finally,

profiles

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“cloud

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the “cloud side” classes are quite similar, with an increased spread in the “cloud side” class.

6. CONCLUSION

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We propose an adaptation of a method of APSD retrieval from multiwavelength lidar by Jagodnicka et al., 2009 to estimate CDNC at the base of a cumulus cloud. The method

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compares the synthetic lidar profiles calculated using the predefined functional form of

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particle size distribution with the experimental profile.

The information from the parcel model, allowing for a physically based description of particle size distribution in a layer in which cloud droplets are activated, is used as supporting

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information in calculations of synthetic lidar profiles. The modified procedure adapted to multiwavelength lidar observations of small cumuli produces realistic values of CDNC. With

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additional assumptions of negligible secondary scattering at the cloud base, the method allows the estimation of the vertical profile of the effective radius of cloud droplets a few tens of meters above the condensation level.

In principle, the comparison of synthetic and measured lidar profiles can be used to estimate the updraft velocity for a given functional shape of an aerosol boundary layer.

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The feasibility study of the retrieval method presented herein calls for the experimental verification with use of airborne measurements of aerosol, cloud droplet number

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concentration and updraft velocity in the cloud base region.

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7. ACKNOWLEDGEMENTS

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The measurements were performed in the Laboratory of Radiative Transfer, University of Warsaw, supported by the Polish Ministry of Science and Higher Education with grant 519/FNiTP/115/2010. Data analysis was supported by the Polish Ministry of Science and Higher Education with the statutory funds for research (2012/13), the Faculty of Physics of the University of Warsaw (Institutes of Experimental Physics and of Geophysics), and the Institute of Applied Optics. We thank Sylwester Arabas for consultations concerning the adiabatic parcel model. We thank anonymous reviewers for detailed and thorough comments, which helped to improve the manuscript.

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ACCEPTED MANUSCRIPT Petters, M.D., Kreidenweis, S.M., 2007. A single parameter representation of hygroscopic growth and cloud condensation nucleus activity. Atmos. Chem. Phys., 7, 1961-1971, doi: 10.5194/acp-7-1961-2007

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Analytical function for lidar geometrical compression form-factor calculations, Appl. Opt. 44, 1323-1331, doi: 10.1364/AO.44.001323

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doi: 10.1364/AO.37.000417

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Highlights We use a three-wavelength lidar to study convective clouds. We use simulations of aerosol activation in rising parcel as constraints for retrievals of cloud droplet number concentration. We demonstrate, that this approach leads to reasonable retrievals of droplet concentrations.