Investigation of Droplet Size Distributions and Drizzle Formation Using A New Trajectory Ensemble Model. Part II: Lucky Parcels

Transcription

1 VOLUME 66 J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S APRIL 2009 Investigation of Droplet Size Distributions and Drizzle Formation Using A New Trajectory Ensemble Model. Part II: Lucky Parcels L. MAGARITZ AND M. PINSKY Department of Atmospheric Sciences, The Hebrew University of Jerusalem, Jerusalem, Israel O. KRASNOV International Research Centre for Telecommunications and Radar, Faculty of Information Technology and Systems, Delft University of Technology, Delft, Netherlands A. KHAIN Department of Atmospheric Sciences, The Hebrew University of Jerusalem, Jerusalem, Israel (Manuscript received 19 March 2008, in final form 4 September 2008) ABSTRACT A novel trajectory ensemble model of the cloud-topped boundary layer containing 1340 Lagrangian parcels moving with a turbulent-like flow with the observed statistical properties was applied to investigate the formation of the microphysical structure of stratocumulus clouds (Sc) in a nonmixing limit (when turbulent mixing between the parcels is not taken into account). The Sc observed in two research flights during the Second Dynamics and Chemistry of the Marine Stratocumulus field study (DYCOMS II) RF01 (no drizzle) and RF07 (weak drizzle) are simulated. The mechanisms leading to a high variability of droplet size distributions (DSDs) with different spectrum width and dispersion are discussed. Drizzle formation was investigated using the radar reflectivity LWC and LWC effective drop radius diagrams simulated by the model in the nondrizzle and drizzle cases. It is shown that in the RF07 case large cloud droplets that trigger drop collisions and drizzle formation form only in a small fraction (about 1%) of the parcels (which will be referred to as lucky parcels) in which LWC exceeds ;1.5 g m 23. This value exceeds the horizontally averaged LWC maximum value of 0.9 g m 23 by two to three standard deviations, indicating a small amount of lucky parcels. In a nondrizzling cloud simulation this threshold is exceeded extremely rarely. The dependence of the threshold value of LWC on aerosol concentration is discussed. The lucky parcels (at least in the nonmixing limit) start their updraft in the vicinity of the surface, where the water vapor mixing ratio is maximum, and ascend to the highest levels close to the cloud top. It is shown that the lucky parcel tracks are related to the large eddies in the boundary layer, which indicates the substantial role of large eddies in drizzle formation. 1. Introduction The precipitating, radiative, and reflectivity properties of warm stratiform clouds strongly depend on the shape of droplet size distributions (DSDs), which can vary substantially at the scales of several tens of meters (Korolev and Mazin 1993; Korolev 1994, 1995). Especially substantial changes of radiative cloud properties Corresponding author address: A. Khain, Department of Atmospheric Sciences, The Hebrew University of Jerusalem, Givat Ram, Jerusalem 91904, Israel. khain@vms.huji.ac.il are related to drizzle formation (e.g., Stevens et al. 1998b; vanzanten et al. 2005; Petters et al. 2006). The microphysical properties of stratocumulus clouds (Sc) have been measured and simulated in a great number of observational and numerical studies (see references in Pinsky et al. 2008, hereafter Part I). Typical vertical profiles of horizontally averaged droplet concentration, liquid water content (LWC), drizzle flux, etc. in nondrizzling and drizzling clouds have been measured (e.g., Wood 2005; Pawlowska et al. 2006). As the observations show, intense drizzle formation starts when the effective radius of droplets exceeds some value that is evaluated by different authors to be from 10 to 14 mm (Gerber DOI: /2008JAS Ó 2009 American Meteorological Society 781

2 782 J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S VOLUME ; Yum and Hudson 2002; vanzanten et al. 2005; Twohy et al. 2005). The dependence of droplet concentration and droplet size on aerosol concentration was widely discussed in the literature (e.g., Twomey 1977; Martin et al. 1994). Based on observations, drizzle parameterizations have been formulated for general circulation models (e.g., Pawlowska and Brenguier 2003), and the dependence of drizzle fluxes on the mean cloud depth and droplet concentration has been proposed (e.g., Gerber 1996; Brenguier et al. 2000). At the same time, however, many fundamental questions concerning the mechanisms of drizzle formation remain without answer. Large-eddy simulation (LES) models have emerged as a powerful tool for simulating the microphysical properties of stratocumulus clouds (e.g., Kogan et al. 1994, 1995; Feingold et al. 1994, 1998a,b; Stevens et al. 1996, 1999, 2005a; Moeng et al. 1996; Khairoutdinov and Kogan 1999, 2000; Khairoutdinov and Randall 2003). We suppose, however, that the Lagrangian approach used in trajectory ensemble models (TEMs; e.g., Stevens et al. 1996; Feingold et al. 1998a; Harrington et al. 2000; Erlick et al. 2005) has some advantages over the Eulerian approach used in the LES models with regard to the investigation of microphysical processes because the Lagrangian approach makes it possible to follow the DSD evolution along the air trajectories and compare the histories of different air parcels forming within the cloud. However, state-of-the-art TEMs do not take into account droplet collisions and sedimentation and cannot be used for the investigation of drizzle formation. In Part I a new TEM is described and successfully applied to reproduce the microphysical properties of stratocumulus clouds observed during research flights RF01 (negligible drizzle fluxes) and RF07 (weak drizzle) in the Second Dynamics and Chemistry of the Marine Stratocumulus field study (DYCOMS II). The specific feature of the model is that a great number of Lagrangian air parcels with a linear size of about 40 m cover the entire boundary layer (BL) area. The parcels are advected by a time-dependent turbulent-like flow generated by a statistical model that reproduces the velocity field with statistical properties derived from observations. A substantial improvement of the approach as compared to that used in state-of-the-art TEMs was the following: the new model took into account both collisions between droplets in each parcel and droplet sedimentation. These improvements make it possible to simulate drizzle formation and the change of drizzle flux during drizzle fall within and below the cloud. The present study is the continuation of Part I and investigates of the physical mechanisms of droplet size distribution and drizzle formation. The main question addressed in this paper is this: To what extent can drizzle formation in stratocumulus clouds be explained in terms of nearly adiabatic trajectories (i.e., where mixing is performed only by sedimentation)? In particular, the following problems will be discussed: (i) What are the mechanisms determining the significant horizontal variability of the DSD shapes and the integral parameters (e.g., LWC, droplet concentration, DSD dispersion) at spatial distances as small as hundred to few hundred meters (e.g., Korolev 1995)? (ii) What are the main microphysical parameters determining the drizzle triggering in stratocumulus clouds? (iii) Why are drizzle fluxes highly nonuniform in the horizontal direction and why do they cover a comparatively small area fraction of stratocumulus clouds that seem to be visibly uniform? Why are the minimum characteristic distances between the neighboring zones of drizzle about 1 km to a few kilometers (Wood 2005; vanzanten et al. 2005)? It is clear that it is impossible to give exhaustive answers to these fundamental questions related to the drizzle formation mechanisms within one paper. Moreover, to identify the main physical mechanisms the analysis will be performed first under simplified conditions, namely in the nonmixing limit (i.e., neglecting turbulent mixing between Lagrangian parcels). It was shown in Part I that many microphysical cloud properties of nondrizzling and drizzling clouds can be realistically simulated even under such simplification. 2. A brief model description The model is described in Part I in detail; hence, only a short description is presented below. The velocity field is represented as the sum of a great number of harmonics with random amplitude and characteristic time scales. The velocity field obeys turbulence laws. The parameters of the model are calculated to obey the correlation properties of the velocity field measured. A great number of Lagrangian parcels with the linear scales of about 40 m are advected by this velocity field. At t 5 0 the volumes of the air parcels were assumed equal, and parcels were distributed uniformly over the whole BL area. At t 5 0 the BL is assumed to be cloud free, so that the parcels contain nonactivated aerosol particles (APs) only. In the ascending parcels crossing the lifting condensation level (LCL), some fraction of aerosols activates and gives rise to droplet formation.

3 APRIL 2009 M AGARITZ ET A L. 783 Hence, nonactivated aerosols and droplets can exist in each cloud parcel. In the course of parcel motion supersaturation in the parcels can increase, which may lead to the nucleation of new droplets and to the formation of bimodal and multimodal DSD. If the supersaturation in a parcel is replaced by undersaturation, droplets evaporate partially or totally. In the latter case the cloud parcel turns out to be droplet free, containing only wet aerosol particles, including those remaining after drop evaporation. Motion of parcels accompanied by condensation/evaporation (heating/cooling) lead to the formation of realistic horizontally averaged vertical profiles of temperature, moisture, and microphysical characteristics in the cloud-topped BL (CTBL). We do not take into account the effects of microphysics on the dynamical (turbulent) structure explicitly. Instead, we generate a turbulent-like dynamical structure that corresponds to that observed in the CTBL. In nature this dynamical structure is formed under the combined effect of many factors: latent heat release, radiation, thermal instability, wind shear, surface heat and moisture fluxes, etc. Assimilating real dynamics, we implicitly take into account all factors affecting the CTBL dynamics. Simulation of turbulent-like flows corresponding to different thermodynamic situations in the CTBL makes it possible to investigate the effects of the BL dynamics, thermodynamics, and aerosol properties on the microphysical structure of stratocumulus clouds. The microphysics of a single Lagrangian parcel (for details, see Pinsky and Khain 2002; Part I) includes the diffusion growth/evaporation equation used for aerosols and water droplets, the equation for supersaturation, and the stochastic collision equation describing collisions between droplets. The mass of aerosols within droplets is calculated as well. The size distribution of cloud particles (both nonactivated nuclei and droplets) is calculated on the mass grid containing 500 bins within the mm radius range. The mass of each bin changes with time (height) in each parcel according to the equation for diffusion growth. A small 0.01-s time step is used to simulate adequately the growth of the smallest APs so that the separation between nonactivated nuclei attaining equilibrium (haze particles) and the growing droplets is simulated explicitly (without any parameterization). The precise method proposed by Bott (1998) is used to solve the stochastic collision equation. The collision droplet growth was calculated using a collision efficiency table with high 1-mm resolution in droplet radii (Pinsky et al. 2001). Drop collisions are calculated with a 1-s time interval. The collisions are calculated on the mass grid formed in the course of the diffusion drop growth/evaporation. The latter decreases numerical broadening of DSDs in the model. The AP budget is calculated in the model. The APs exist in two states : (i) nonactivated wet AP (haze particles) and (ii) APs dissolved within droplets. The mass of APs in droplets does not change during condensation/evaporation process. Each act of drop collisions leads to an increase of the dissolved AP mass in the drop collectors. The droplet evaporation leads to the formation of wet APs. Thus, drop collisions change the AP size distribution during the parcel recirculation within the BL. The distinctive feature of the model is the accounting for droplet sedimentation (see Part I for details). To calculate drop fluxes between parcels, the computational area was covered by regular grid with a resolution of 5 m. The 5-m length segments belonging to one and the same parcel are characterized by the same values of thermodynamic parameters. The algorithm of sedimentation actually represents an extension of the widely used flux method (e.g., Bryan 1966; Bott 1989), describing advection and sedimentation in the Eulerian models with irregular finite difference grids, to the grid formed by the centers of the parcels. In this sense, the model can be referred to as the hybrid Lagrangian Eulerian model. The main dynamical and microphysical parameters of the model are presented in Table 1. Note that there are many dynamical and thermodynamic processes affecting the structure of the cloud-topped BL (radiative processes, surface fluxes, entrainment of dry air from above, etc.). As was mentioned in Part I, characteristic time scales of these processes are longer than those of turnover time; thus, as a first step we limit the simulations to the analysis of the strongest and fastest effects related to the vertical motions of parcels that mix the BL and lead to cloud formation. 3. Design of numerical experiments and data assimilation To analyze the DSD formation mechanisms in both nondrizzling and drizzling stratocumulus clouds, we have simulated stratocumulus clouds observed during two research flights conducted as part of the DYCOMS II field experiment, RF01 (negligible drizzle at the surface) and RF07 (a weakly drizzling cloud). The investigation of the Sc observed in these flights makes it possible to determine the necessary conditions (demarcation) for drizzle formation. The corresponding numerical simulations are referred to as the RF01 and the RF07 runs, respectively. In both cases the cloud top height was about 850 m (Stevens et al. 2003a,b, 2005a). The ridged upper boundary is identified with the temperature inversion at this level. To reproduce the

4 784 J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S VOLUME 66 TABLE 1. The main model parameters used in the simulations. Dynamic and geometric parameters Microphysical and thermodynamic parameters Characteristic size of air parcels (m) ;40 No. of mass bins 500 No. of parcels 1344 Range of cloud particles (mm) Length of the area L (m) 2550 Time step of diffusion growth (s) 0.01 Height of the area H (m) 850 Time step for collisions (s) 1.0 No. of harmonics M 5 N 50 Time step for sedimentation (s) 1.0 Max rms vertical velocity fluctuation (m s 21 ) 0.7 Chemical composition of aerosols NaCl Lifetime of harmonics (s) Surface temperature (K) (RF01) (RF07) Time period of velocity field updating (s) 0.1 Turbulent dissipation rate (cm 2 s 23 ) 10 statistical properties of the velocity field, which were similar for both flights, the structure function measured by Lothon et al. (2005) for the conditions of flight RF07 was applied for both simulations. The amplitudes of the harmonics were calculated to reproduce the observed profile of turbulent vertical velocity variation hw 02 i (Stevens et al. 2005a). The harmonics of the largest scales represent large eddies, which usually exist in the cloudy and cloud-free BL (e.g., LeMone 1973; Ivanov and Khain 1975, 1976; Stevens et al. 1996). To perform the simulations, both dynamical and thermodynamic parameters were adopted as discussed in detail in Part I. The specific feature of the flights under consideration was that many parameters (such as the droplet concentrations, sea surface temperatures, cloud top heights, etc.) were quite similar (see Table 2). The main difference between the conditions was the difference in the mean specific humidity: 9 g kg 21 in RF01 versus 10 g kg 21 in RF07, which determined the difference between the cloud base height: 585 m in RF01 and 310 m in RF07. As was mentioned above, the purpose of the simulation was to form clouds in the initially noncloudy BL by vertical mixing of the BL with air parcels. Correspondingly, at t 5 0 the relative humidity (RH) in all parcels was set less than 100%. Hence, we could not use the vertical temperature and humidity profiles observed in the cloudy BL as the initial ones. On the contrary, the model itself generated profiles close to the observed ones as a result of the BL mixing by motion of the parcels. Because the amount of the total water content (water vapor 1 liquid water) is conserved in the BL during the process of vertical mixing and condensation, the initial mixing ratio profiles were chosen so as to have mean values of 9 and 10 g kg 21 to simulate clouds in RF01 and RF07, respectively. Similar considerations were applied for the choice of initial temperature profiles. It was quite important in such a choice to get the RH within the BL and the cloud base heights close to observations. Supplemental simulations indicate that the sensitivity of the temperature profile after the model spinup to the choice of the initial temperature gradient is weak because vertical BL mixing leads to the dry adiabatic temperature gradient below cloud base and nudges the temperature gradient to the moist adiabatic aloft. The initial profiles of the mixing ratio and the liquid water static energy temperature used in the model, as well as the changes of these profiles with time, are shown in Figs. 1 and 2, respectively. At t 5 0 the aerosol size distributions in all parcels were assumed to be similar. These distributions were taken from in situ measurements (Fig. 3). 4. Formation of the cloud microphysical structure a. Spatial inhomogeneity of the integral parameters As was shown in Part I, the model reproduces well the vertical profiles of specific humidity, LWC, drizzle size, and averaged drizzle fluxes, as well as the radar reflectivity. As an example, we present Figs. 4 and 5, which compare the measured and simulated vertical profiles of the LWC in the RF01 and RF07 cases, respectively. Simulated profiles are plotted with an increment of 5 min. One can see that the mean LWC in the RF07 case exceeds that in the RF01 case both in observations and simulations. In the RF01 case the model overestimates the maximum values of LWC, supposedly because of some overestimation of the BL humidity. As a result, in this case the cloud base is about 100 m lower than in the observations. In the RF07 there is a good agreement in the cloud base height between observations and the model results. Nevertheless, the maximum values of LWC calculated in the model are larger than those measured by the Gerber and the King probes. We attribute this difference to the following reasons. It is a known fact that the King and the Gerber probes work correctly only when the droplet size is less than some threshold value (about ;15 mm) and tend to underestimate LWC in the presence of larger drops (see Wendisch et al. 2002; Korolev et al. 1998; Gerber 2001). One can expect that in the presence of drizzle more

5 APRIL 2009 M AGARITZ ET A L. 785 TABLE 2. Comparison of calculated values with those measured in flights RF01 and RF07. Flight RF01 No drizzle case Flight RF07 Drizzle case Cloud base 585 m m 310 m m q t 9gkg g kg g kg g kg 21 LWC max 0.5 g kg g kg g kg g kg 21 Drizzle flux Below detection level Below detection level 0.6 (60.18) mm day mm day 21 Droplet concentration ;150 cm 23 ;190 cm 23 ;150 cm 23 ;160 cm 23 The range of effective radii at 820 m mm 8 12 mm mm mm Mean effective radius of DSD near the surface No drizzle 75 mm 100 mm 100 mm Max effective radius near the surface No drizzle 100 mm 160 mm 200 mm Max radar reflectivity 212 dbz 212 dbz 4 5 dbz 4 5 dbz accurate LWC values can be derived from the DSD measured spectral probes such as the Passive Cavity Aerosol Spectrometer Probe (PCASP), the Forward Scattering Spectrometer Probes (FSSP)-100 and FSSP- 300, the Particle Measuring System (PMS)-260X probe, and the 2D cloud probe (2DC). The data obtained using these probes in RF01 and RF07 were synchronized and averaged into a 10-s time grid. The merging methodology of the DSD measured with different probes has been described by Baedi et al. (2000), Krasnov and Russchenberg (2002), and Khain et al. (2008). The height dependence of the LWC derived from the measured DSD ispresentedinfig.5c.onecanseethatthelwcobtained in the model agrees well with the LWC values derived from the DSD measurements. Several specific features are seen in Figs. 4 and 5. First, there is a good agreement between the averaged LWC values as well as between the slopes of the FIG. 1. The horizontally averaged profiles of the mixing ratio (a),(c) as measured in the research flights RF01 and RF07 and (b),(d) as calculated at different time instances in the corresponding simulations. The profiles are plotted with a time interval of 5 min. Dashed lines in (b) and (d) are initial profiles and are marked as t 5 0; (a) is adopted from Faloona et al. (2005) and (c) is adopted from Stevens et al. (2003b).

6 786 J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S VOLUME 66 FIG. 2. Vertical profiles of liquid water static energy temperature (a) from Flight RF01 (after Stevens et al. 2003b) and (b),(c) from model simulations (b) RF01 and (c) RF07. A good agreement of the profile obtained in the RF01 run with the observations in RF01 is seen. Profiles are plotted with increments of 5 min. The dashed lines in (b) and (c) indicate the initial profiles at t 5 0. averaged height dependencies of LWC measured in situ, calculated using the measured DSD and simulated by the model. Second, the values of LWC calculated using measured DSD vary within a range significantly wider than those in the case of the Gerber and King probes. One can see from Fig. 5c that the maximum values significantly exceed the mean values. This feature is well reproduced by the model. The third feature is that the LWC obtained from observations is nonzero near the surface even in the nondrizzling RF01 case (the King probe; Fig. 4). In the RF07 case this feature is clearly seen in Figs. 5b,c. The model successfully reproduces these observations. FIG. 3. Size distributions of dry aerosols in RF01 and RF07 flights used in the simulations. The distributions are a composite from a radial differential mobility analyzer and a passive cavity aerosol spectrometer probe. Figure 6 shows the horizontal variations of the LWC, droplet concentration, DSD width, and DSD dispersion (the ratio of the DSD width and the mean radius) at z m in the RF07 and RF01 model runs, respectively. One can see high variability of all parameters with significant changes at distances of 100 to a few hundred meters. Such variability has been found to be a typical feature of stratocumulus clouds (Korolev 1995). The spatial variability in the nondrizzling RF01 run is even stronger because noncloudy parcels cover larger areas above the geometric cloud base in this run. Figure 7 shows the normalized horizontal correlation functions B(x) of the LWC, droplet concentration, vertical velocity, and radar reflectivity calculated at the levels of 500, 650, and 800 m in both the (left) RF01 and (right) RF07 runs. The values of the integral spatial scale, determined as L o 5 1/B(0) Ð 0 jb(x) jdx, are presented in the figure as well. One can see that the droplet concentration has the minimum L o (ranging from 60 to 75 m) whereas the radar reflectivity has the maximum L o (ranging from 120 to 217 m). Near the cloud base the LWC has the same L o as the drop concentration. However, in the vicinity of the cloud top the integral scale of the LWC increases. We attribute the differences between the integral scales of these quantities to the following: Droplet concentration is the zero moment of the DSD; thus, any vertical shift of the parcels can lead to nucleation or evaporation of small droplets, which can affect droplet concentration but may not affect LWC significantly. The LWC is the third moment of the DSD, which is a more inertial parameter as compared to the droplet concentration. The characteristic time of condensation determining variation of the LWC is larger than that of nucleation. The vertical velocity fluctuations decrease toward the cloud top. The latter

7 APRIL 2009 M AGARITZ ET A L. 787 FIG. 4. (a),(b) Vertical profiles of the LWC measured by (a) the Gerber probe and (b) the King probe; (c) LWC derived using measured DSD in the RF01 case. The low right panel shows the horizontally averaged LWC obtained in the model simulation of the RF01 case. Simulated profiles are plotted with an increment of 5 min; the dashed line indicates the averaged LWC profile obtained in 10 LES simulations (Stevens et al. 2005a). can be one of the reasons of the increase in the integral scales of concentration, especially for LWC with height (this mechanism is discussed in more detail in section 4d). The radar reflectivity (the sixth moment of the DSD) reflects the existence of large drops. The characteristic time of the radar reflectivity variation also includes the time for collisions and exceeds the characteristic time of the condensation. The reflectivity has the integral scale, which is quite close to that of the vertical velocity. This large integral scale reflects the fact that fluctuations of the radar reflectivity are caused by the fluctuations of the large-scale most energetic velocity harmonic (large eddies; see below). Note that the integral spatial scale of the turbulent velocity field was taken as 158 m (Lothon et al. 2005). The variability of the LWC and concentration is often attributed to nonadiabatic processes, such as parcel mixing or the dilution by dry air penetrating through the cloud top and drizzle loss (Stevens et al. 1998a; Wood 2005). Note that in the RF01 model run all parcels are close to adiabatic (very weak droplet sedimentation and no turbulent mixing with the neighboring parcels). Nevertheless, the DSD dispersion in the RF01 run is actually similar to that in the RF07 run. Thus, the nonadiabatic processes do not play a dominant role in the formation of the DSD and of DSD variability. The mechanisms responsible for the DSD formation will be discussed in the next section. b. DSD formation As can be seen in Figs. 6 and 8, the average value of the DSD dispersion is about , and droplet spectrum width is about 2 mm, which is in a good agreement with the observations in stratocumulus clouds (e.g., Martin et al. 1994; Pawlowska et al. 2006). At the same time the dispersion actually varies in the simulations within a wide range from 0.1 to about 1.0 (Fig. 9). There were many attempts to explain the DSD broadening within the frame of the stochastic condensation theory (see review by Khain et al. 2000). The simplified

8 788 J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S VOLUME 66 FIG. 5. As in Fig. 4, but for the RF07 case. Dashed lines indicate the slope of the averaged height dependence of LWC as measured and simulated by the model. equation for diffusion/evaporation in which curvature and chemical terms are neglected implies that the DSD in ascending and in descending branches of the parcel trajectory should be similar at the same height level. The latter creates problems regarding the explanation of the horizontal variability of the DSD parameters observed in situ. Korolev (1995) showed that accounting for these terms in the equation for the diffusion growth introduces some asymmetry into the diffusion growth and evaporation processes and leads to the DSD broadening. However, the asymmetry becomes visible after a great number of successive updrafts and downdrafts of a parcel within the cloud layer; hence, this mechanism is not efficient. Another mechanism leading to the DSD broadening is the secondary drop nucleation (Korolev and Mazin 1993; Korolev 1994; Pinsky and Khain 2002; Segal et al. 2003), when supersaturation in an ascending parcel exceeds that at the lifting condensation level. It is clear that if the secondary droplet nucleation takes place, the DSDs in the ascending and descending branches of the parcel trajectory differ. We will discuss here two other mechanisms leading to a dramatic difference between the DSD parameters in the ascending and descending branches of the parcel trajectory in Sc. As a first example, we take a parcel beginning its ascent below the geometric cloud base, whose height time dependence is shown in Fig. 10. The DSDs in this parcel at different points along the trajectory are shown as well. The values of supersaturation, LWC, drop concentration, and DSD dispersion along the parcel track are presented in Table 3. The LCL of this parcel is ;300 m and the parcel rapidly ascends to the upper levels (800 m). Above 300 m the DSD dispersion first rapidly decreases to 0.07 in agreement with the equation for the diffusion growth and then slightly increases by appearance of the smallest droplets with the increase in

9 APRIL 2009 M AGARITZ ET A L. 789 FIG. 6. The horizontal cross sections of the LWC, droplet concentration, DSD width, and DSD dispersion at z m at t 5 35 min in the simulations (top) RF07 and (bottom) RF01. supersaturation and droplet sedimentation from above. The parcel is located near the cloud top for about 20 min. During the horizontal motion the DSD changes, and larger drops (up to the 20-mm radius) form by droplet collisions. As was shown by Pinsky and Khain (2002), droplet collisions (even when not efficient) play a very important role at the stage usually referred to as the diffusion growth stage, leading to the formation of drops of a size larger than could be obtained by diffusion growth only. Further parcel descending leads to a dramatic growth of the DSD dispersion in the parcel because of a significant decrease in the size of small

10 790 J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S VOLUME 66 FIG. 7. The correlation functions of the LWC, droplet concentration, vertical velocity, and radar reflectivity calculated at the levels of 500, 650, and 800 m in (left) RF01 and (right) RF07. Values of the integral correlation scale are presented in the panels. droplets owing to evaporation, whereas the size of the largest droplets decreases much less. As a result, the DSDs as well as all their characteristics (including the DSD dispersion) turn out to be different at the same levels within the parcel updraft and downdraft branches. Thus, existing of collisions between droplets and succeeding evaporation make the DSD in updraft and downdrafts significantly different, increasing the average DSD width and dispersion. The existence of small droplets with the radii below ;5 mm inscatsignificant distances above the cloud base is a well-established observational fact (Nicholls 1984; Khairoutdinov and Kogan 1999). Both secondary droplet nucleation and partial droplet evaporation in the downdrafts can be mechanisms explaining this effect. Figure 11 shows that the DSD dispersion in ascending parcels is as a rule smaller than in descending ones. One of the reasons is the effect of droplet collisions. Figure 12 presents another example of an air parcel. The variations of different parameters along the parcel track are presented in Table 4. Initially the parcel was located in the upper half of the BL (it was initially a noncloudy one). The parcel first moves down and then ascends. Below the LCL the size distribution is formed by haze particles (nonactivated aerosols). The largest radius of the wet particles exceeds 10 mm, which corresponds to the largest size of dry aerosols of 1.3 mm in the aerosol spectrum (Fig. 3). Because the mean radius is very small, the dispersion of the wet aerosols spectrum is large (0.96). The parcel crosses its LCL in the upper half of the BL (slightly above 600 m), indicating the formation of new cloudy parcels within the cloud layer. Because the

11 APRIL 2009 M AGARITZ ET A L. 791 FIG. 8. Vertical profiles of (left) the horizontally averaged droplet spectrum width and (right) the droplet spectrum dispersion at t min in the RF01 and RF07 runs. mean droplet radius is small just above the LCL, the DSD dispersion is large (0.4). Then the dispersion decreases to 0.1 because of diffusion growth and starts increasing because of collisions and new drop nucleation. The histogram of the LCL of the parcels in the RF07 run is shown in Fig. 13. The existence of parcels with low LCL is determined by high air humidity preset in all parcels at t 5 0. The presence of such parcels with an LCL significantly lower than cloud base height is seen in Figs. 4 and 5 both in the measurements and model results. The number of parcels with low LCL decreases with time. The number of parcels with the LCL above the geometrical cloud base remains significant. Droplet sedimentation and collisions lead to the fact that the LCL of a parcel does not coincide with the level of total droplet evaporation in downdrafts. It means that the FIG. 9. Histograms of droplet spectra dispersion in clouds simulated in the (left) RF01 and (right) RF07 runs at the levels located above z m at t min.

12 792 J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S VOLUME 66 FIG. 10. Time dependence of the height location of one of the parcels in the RF07 run. The DSDs are presented in several points along the trajectory. The values of supersaturation, LWC, drop concentration, and DSD dispersion at these instances are presented in Table 3.

13 APRIL 2009 M AGARITZ ET A L. 793 Panel TABLE 3. Parameters of the parcel presented in Fig. 10. Time Supersaturation (min) (%) LWC Concentration (g m 23 ) (cm 23 ) Drop dispersion a b c d e f DSD will be different at one and the same height level. Thus, the secondary droplet nucleation, droplet collisions, and formation and disappearance of cloudy parcels at different heights within the cloud layer lead to a high spatial inhomogeneity of cloud parameters, as well as to high values of the mean DSD dispersion. c. Lucky parcels and their parameters The high inhomogeneity of DSD parameters in Sc shows that drizzle cannot form in all parcels at the same time. Moreover, many parcels cannot produce drizzle during their short residential time in the cloud, and all (or most) droplets evaporate in these parcels in downdrafts without reaching the size required for collision triggering. This statement agrees with the observations showing that as a rule drizzle covers a comparatively small area of stratiform clouds (e.g., Stevens et al. 2003a,b, 2005b; Wood 2005). It is especially valid for light drizzling Sc (such as in the RF07 flight). The latter suggests the existence of parcels in which large droplets exceed some critical size and trigger droplet collisions, leading to drizzle formation. The largest drops fall down and collect smaller ones in the parcels located below. The parcels in which intense droplet collisions is first triggered will be referred to here as lucky parcels. Because the droplets fall from the lucky parcels, these parcels can be also referred to as donors (Khain et al. 2008). The parcels in which collisions take place because of large drops penetrating from above will be referred to as acceptors. In a general case, parcels can be both donors and acceptors, which makes it difficult to find lucky parcels and reveal their properties. To perform such analysis, a supplemental simulation RF07_no_sed has been carried out with no droplet sedimentation included. Because we are looking for parcels in which intense collisions have just started, the droplet sedimentation should not be considered an important factor at this stage. Hence, we suppose that the properties of lucky parcels found in the simulations without drop sedimentation will be valid in a more general case when droplet sedimentation is taken into account. FIG. 11. Average drop dispersion in the RF07 run in the updraft and downdraft zones. As shown by Krasnov and Russchenberg (2002), Khain et al. (2008), and Part I, the analysis of radar reflectivity LWC diagrams (hereafter, the Z LWC diagrams) is an efficient tool to investigate microphysical processes in clouds. Figure 14 shows the Z LWC diagrams at t 5 25 min, t 5 30 min, t 5 35 min, and t 5 40 min in the RF07_no_sed run. One can distinguish three main zones on this diagram. The first zone corresponds to the stage of the diffusion growth, when Z is small (less than 210 dbz) and the LWC growth leads to the growth of Z (zone 1 in the figure). The second zone with Z.210 dbz corresponds to the beginning of intense collisions and drizzle formation. In this zone the sharp growth of Z takes place under the nearly constant LWC (zone 2 in the figure). Zone 3 is formed by descending parcels, in some of which intense collisions are accompanied by partial drop evaporation (i.e., by a decrease in LWC). One can see that intense collisions start in the parcels with the LWC exceeding about 1.5 g m 23. These parcels are located near the cloud top. One can also see that the radar reflectivity of 210 dbz can serve as a threshold separating Sc in which drizzle is produced from those in which drizzle does not form. To show at which effective radii intense collisions are triggered, we present Fig. 15 where the relationship LWC 2 r eff in the RF07_no_sed run is shown at 25, 30, and 35 min. The arrows in the figure show the shift of the corresponding parcels in the LWC 2 r eff diagram during the previous 5-min period. In Fig. 15 one can identify the same zones that were seen in Fig. 14. In parcels forming zone 1, the diffusion growth dominates; zone 2 is formed by the parcels in which intense collisions are triggered and drizzle is forming. Zone 3 is formed by descending parcels in which small droplets

14 794 J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S VOLUME 66 FIG. 12. As in Fig. 10, but for the parcel initially located at z m. The values of supersaturation, LWC, drop concentration, and DSD dispersion at these instances are presented in Table 4.

15 APRIL 2009 M AGARITZ ET A L. 795 Panel TABLE 4. Parameters of the parcel presented in Fig. 12. Time Supersaturation (min) (%) LWC Concentration (g m 23 ) (cm 23 ) Drop dispersion a b c d e f evaporate, which results in a rapid increase in r eff. During the diffusion growth, the effective radius increases with the LWC monotonically. The start of intense collisions is seen by the increase in r eff under nearly the same LWC. One can see that intense collisions start when LWC exceeds ;1.5 g m 23 and r eff exceeds about mm. These values of r eff are in good agreement with observations (Gerber 1996; vanzanten et al. 2005; Twohy et al. 2005), as well as with the results of detailed numerical simulations of the DSD formation in an ascending cloud parcel (Pinsky and Khain 2002). The decrease in the LWC and strong increase in r eff that is seen in zone 3 is related to the descent of corresponding parcels, accompanied by the evaporation of the smallest droplets in the DSD. Figure 16 shows the LWC drizzle drop concentration relationships along the trajectories of several parcels in the RF07_no_sed run. One can see that a very small amount of large droplets forms even at comparatively small LWC. However, at small LWC these droplets cannot trigger intense drizzle formation, and the increase in the mean and effective radius is related to the diffusion growth (see Pinsky and Khain 2002 for detail). In most parcels LWC does not reach the values necessary for collision triggering. When these parcels start descending, both the LWC and the large drop concentration decreases. The line of red arrows illustrates changes in the LWC and the concentration of large droplets each 5 min in one of the lucky parcels. Triggering of large droplets formation takes place when the LWC exceeds 1.5 g m 23 (Fig. 16, right-hand side). Figures indicate that the rapid formation of large drops (drizzle) by collisions takes place when the LWC exceeds about 1.5 g m 23. It should be noted that such high values of LWC in the RF07 run are reached only in a small fraction of cloud parcels. The maximum value of the mean horizontally averaged LWC in the RF07 run is about 0.9 g m 23 (Fig. 5). The formation of lucky parcels corresponds to the positive fluctuations of the LWC that can exceed two LWC standard deviations. Figure 17 shows the LWC histogram in the drizzling (RF07) run plotted for all parcels located above 600 m in the entire simulation. Note first that there is a significant FIG. 13. The histograms of the lifting condensation level heights of parcels in the RF07 run at t. 30 min. One can see that a significant number of the parcels become cloudy parcels above 500 m (the geometric cloud base). amount of noncloudy parcels with negligible LWC above the 600-m level. The existence of such parcels (noncloudy volumes) within the stratocumulus layer and their role in the formation of mean DSD parameters were discussed in section 4b. One can also see that the fraction of the parcels with the LWC. 1.5 g m 23 is about 0.6% among the cloud parcels and about 0.3% of total parcel amount. Because the conclusion that there are such large LWC values under DYCOMS II conditions is quite important for both model justification and the understanding of the drizzle formation, we present Fig. 18 comparing the LWC diagrams calculated by the model and calculated using the LWC values derived from the measured DSD. The panels presented in the left column depict the histograms for LWC. 0.4 g m 23. Panels presented in the right columns are zoomed histograms showing the tail of the LWC distribution with LWC. 1gm 23. Because numbers of samples are different in measurements and in the model, the histograms were normalized by the maximum value within the LWC range considered. One can see that the shape of histograms obtained in the model actually coincides with that obtained using measured DSD. The maximum is located at LWC g m 23. Analysis shows that the fraction of samples with LWC. 1.5 g m 23 among the total number of samples calculated using the measured DSD is about 0.3% of total number of samples, which is in the excellent agreement with results of simulations. Note that in the RF01 measurements the LWC does not exceed 0.55 g m 23. In the simulations of the RF01 case the number of parcels containing LWC. 1.5 g m 23 is negligible (not shown).

16 796 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 66 FIG. 14. The Z LWC diagram at t 5 25 min, 30 min, 35 min, and 40 min in the RF07_no_sed run. The colors denote the height of parcel location. Numbers in the figures denote zones corresponding to different microphysical processes: zone 1 represents the diffusion growth, whereas in parcels belonging to zone 2 intense collisions and drizzle formation takes place. Zone 3 is formed by descending parcels in which LWC decreases by evaporation. One can see that drizzle formation begins in parcels with LWC exceeding ;1.5 g m23. These parcels are located near the cloud top. We consider the value of LWC ; 1.5 g m23 as a threshold value that should be exceeded for drizzle formation (for the aerosol conditions of the RF01 and RF07 cases). The Sc observed in the RF07 observations is a weak drizzle cloud. Thus, the fraction of lucky parcels in the Sc producing light drizzle can be evaluated as ;1%. On the one hand, this result shows that drizzle in the Sc is triggered by a small number of lucky parcels. On the other hand, we assume that to produce heavy drizzle, Sc must have a fraction of lucky parcels higher than 1%. Note in this connection the difficulties that arise in the simulation of the drizzle formation in the 1D models of CTBL, which use horizontally averaged values of the parameters (see also the comments by Stevens et al. 1998a). According to our results, drizzle can hardly form under an LWC equal to the horizontally averaged values in drizzling stratocumulus clouds. The question here is What are the specific features of parcels in which LWC can exceed 1.5 g m23 in the RF07 case? Note first that the LWC in parcels in- creases with height during ascent; the LWC can exceed 1.5 g m23 only in the parcels reaching the cloud top, as was shown in Fig. 14. However, as can be seen in Fig. 6, the LWC near the cloud top also varies with space and time. So, additional factors exist (e.g., the specific initial parcel location in which the mixing ratio is high). In our simulations the parcels with the maximum values of the mixing ratio were located near the surface (which is quite a typical feature of the BL). Figure 19 supports the assumption concerning an important specific feature of the lucky parcels, namely that they are initially located near the surface. Furthermore, a high value of LWC must exist in a parcel for a certain period of time required for collisions to form large drops (Pinsky and Khain 2002). An increase in the residential time (determined here as the time during which supersaturation in a parcel is positive) favors the formation of the largest drops in the DSD (i.e., fosters the collision triggering; Feingold et al. 1996). The analysis shows that parcels with the largest LWC and the largest effective radii have as a rule a

17 APRIL 2009 M AGARITZ ET A L. 797 FIG. 15. The LWC r eff scattering diagrams in the RF07_no_sed run at t 5 (top) 25, (middle) 30, and (bottom) 35 min. The arrows show the shift of corresponding parcels on the diagrams during the past 5 min. Numbers denote the same zones as in Fig. 12. One can see that triggering of intense collisions begins when LWC exceeds 1.5 g m 23 and the effective radius exceeds mm. longer residence time. Whereas the residence time for most parcels is about 10 min, the parcels in which the LWC exceeds 1.5 g m 23 have residence time of min (Fig. 20). Such correlation between high LWC and the long residential time can be attributed to the following: Parcels with high LWC values are parcels that reach high levels near the cloud top where vertical velocities are small. Hence, the parcels reaching high levels (where small positive supersaturation takes place) tend to remain at these levels longer. In the parcels that do not reach higher levels, positive supersaturation is replaced by a negative one with the change of the vertical velocity sign. We assume that the increase in the spatial radius of correlation with the height for LWC (Fig. 6) can be related to this effect. Thus, it appears that the condition LWC. 1.5 g m 23 in most cases can serve as a condition sufficient for drizzle formation triggering (under conditions of RF01 and RF07). The scheme presented in Fig. 21 summarizes the results concerning the specific features of the lucky parcels. Most parcels starting from lower levels do not reach the highest levels of the cloud and instead start descending, which leads to a decrease in the LWC and drop concentration. The fraction of the parcels with higher LWC and low residential time (which start descending just after they have reached the cloud top) is comparatively small. A great number of the parcels starting at higher levels have a low initial mixing ratio, which is not enough to produce high LWC. Only a small amount of the parcels can become lucky and produce drizzle. It appears that the trajectories of lucky parcels are determined by the outermost streamlines of the large eddies. d. Drizzle fluxes After drizzle formation near the cloud top, the evolution of the DSD continues according to several mechanisms (see Khain et al. 2008; Part I). According to the first mechanism, drizzle falls down from the parcel donors and can collect small droplets within parcel acceptors. As a result, the radar reflectivity in the parcels with low LWC sharply increases. At the same time, parcel donors lose a part of their large drops, so that the radar reflectivity in these parcels decreases together with the decrease in the LWC. As a result of all of these processes, a zone forms in the lower part of the BL, where large values of Z are accompanied by comparatively small values of LWC. This zone is denoted as zone 3 in the Z LWC diagram (Fig. 22). In study by Khain et al. (2008) this zone is associated with the drizzle stage of the Sc evolution. A detailed analysis of drizzle evolution using the Z LWC diagrams is presented by Khain et al. (2008) and in Part I. Here we are interested in the relationship between drizzle fluxes and the velocity field. As was shown in section

18 798 J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S VOLUME 66 FIG. 16. The LWC drizzle drop concentration relationship calculated along the tracks of six different parcels in the RF07_no_sed run during the first t 5 35 min. The arrows indicate the changes in the parcel location on the diagram for the previous 15 min. The line of red arrows (labeled 6) illustrates the changes in the LWC and the concentration of large droplets in one of the lucky parcels. A significant concentration of large droplets is reached when the LWC exceeds 1.5 g m 23 (see the right panel). 4c, the lucky parcels start their ascent in the vicinity of the surface and ascend to the upper levels close to the cloud top. Such updrafts are, supposedly, related to large eddies in the BL, which makes the role of these eddies highly important for drizzle formation. The characteristic size of the large eddies is about 1 km (i.e., on the same order as the BL depth scale). If we take into account the characteristic aspect ratios of large eddies (2 3), the distance of 1 2 km must be close to the minimum intermittent distance between the neighboring zones of significant drizzle fluxes. It seems that this conclusion is supported by observations of Sc (Wood 2005; vanzanten et al. 2005). Fig. 23 shows the changes in the horizontal direction of the drizzle flux at z m and z m and in the vertical velocity at z m in the RF07 run at t min, when the maximum drizzle flux takes place. One can see that the zones of strong drizzle flux (determined as F driz 5 Ð 1mm N(r)m(r)[W V t(r)]dr,wheren(r), m(r), and V r (r) are the concentration, mass, and sedimentation velocity of drop with radius r, andw is the air vertical velocity) coincide well with zones of strong downdrafts caused by the most powerful harmonic representing large eddies. This result supposedly explains why the correlation radii of the vertical velocity and the radar reflectivity are very close (Fig. 7). This result also supports the scheme of drizzle formation plotted in Fig. 21. The influence of the vertical velocity field on the spatial distribution drizzle fluxes requires additional investigation. Figure 24 shows the vertical profiles of horizontally averaged drizzle flux (Fig. 24a), and the concentration of droplets with radii larger than 20, 25, and 40 mm, respectively (Figs. 24b d), at several time instances corresponding to the beginning of drizzle formation (50 min), drizzle increase (70 min), and the maximum drizzle fluxes ( min). As discussed above, drizzle is triggered near the cloud top, where concentration of small drizzle droplets is maximal. Further growth of the drizzle flux depends on the liquid water path in the FIG. 17. The LWC histogram in the drizzling (RF07) run plotted for all parcels above 600 m in the entire simulation. The fraction of parcels with LWC. 1.5 g m 23 is about 1% of cloud parcels in the drizzling cloud. One can see also that there are parcels with negligible LWC (noncloudy parcels) above the 600-m level.

19 APRIL 2009 M AGARITZ ET A L. 799 FIG. 18. The LWC histograms (top) calculated using measured DSD and (bottom) simulated by the model. Panels presented in the left column depict the histograms for LWC. 0.4 g m 23. Panels presented in the right columns are zoomed histograms showing the tail if the LWC distribution with LWC. 1gm 23. The histograms are normalized by the maximum value within the LWC range considered. The zoomed histogram (LWC. 1gm 23 ) was calculated from the merged DSD using 558 samples out of (2.8%). FIG. 19. The LWC mean radius diagram in the RF07_no_sed run at t 5 35 min. In (a) the colors indicate the parcel initial height (at t 5 0). In (b) the color indicates the height of the parcel at t 5 35 min. One can see that the parcels with large LWC (lucky parcels) start at t 5 0 near the surface (where the mixing ratio was maximum) and reach the top levels of the cloud.

20 800 J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S VOLUME 66 FIG. 20. The LWC r eff scattering diagrams in the RF07 run at t 5 35 min. Colors indicate the parcel residence time. One can see that the parcels with highest LWC and the largest effective radii have longer residence times. cloud and, consequently, on the cloud depth. The concentration of drops with radii over 40 mm is maximal near cloud base. The shape of vertical profiles of drizzle fluxes is in a good agreement with those derived by Wood (2005) from observations in stratocumulus clouds. The fluxes decrease below the cloud base because of evaporation. The drizzle flux at the surface depends on the balance between the drizzle flux growth within the cloud and drizzle evaporation. In the RF01 run there is a very small amount of drizzle at the cloud base and it fully evaporates below the cloud, so no drizzle reaches the surface. In the RF07 run the drizzle flux decreases by evaporation by 40% 50%, which agrees with evaluations presented in vanzanten et al. (2005) for drizzling clouds measured during DYCOMS II. 5. Discussion and conclusions In Part I of the study a novel trajectory ensemble model (TEM) of a cloud-topped boundary layer was presented in which a great number of Lagrangian parcels move with a turbulent-like flow with the observed statistical properties. The model was applied to the simulation of stratocumulus clouds observed in two research flights, RF01 (no drizzle) and RF07 (weak drizzle), conducted during the field experiment DYCOMS II. It was shown that the model reproduced well the vertical profiles of horizontally averaged quantities such as the absolute air humidity, the droplet concentration, and LWC, as well as the drizzle drop size and drizzle flux. The present study is a continuation of Part I. It is dedicated to the investigation of the microphysical structure formation of Sc in a nonmixing limit (when no turbulent mixing between Lagrangian parcels is taken FIG. 21. The conceptual scheme of the parcel tracks separating lucky and nonlucky parcels in the nonmixing limit. Lucky parcels start ascending near the surface and reach the heights close to the cloud top. Lucky parcels have a significant residence time with the high LWC. into account). It was shown that to a large extent drizzle formation in stratocumulus can be explained in terms of nearly adiabatic trajectories (i.e., where mixing is limited to that associated with hydrometeor exchange by sedimentation). It is shown that the spatial variability of microphysical parameters is determined by several mechanisms: the secondary droplet nucleation above the lifting condensation level, droplet collisions, and the formation/disappearance of droplets in parcels within the cloud layer. These factors lead to a dramatic difference between the DSD parameters in the ascending and descending branches of the parcel motion. These mechanisms lead to a high spatial variability of the DSDs, with a mean width and dispersion similar to those observed in situ. We would like to especially stress the importance of droplet collisions, which (being comparatively nonintense) lead to formation of largest cloud droplets, which in turn initiate drizzle formation. In this sense, the increase in the collision rate induced by turbulence may be important for acceleration of drizzle formation, in spite of the weak turbulence intensity. Drizzle formation was investigated using the Z LWC and LWC 2 r eff diagrams calculated by the model in nondrizzle and drizzle cases (including the simulation in which drop sedimentation was switched off). The analysis showed the following: (i) Collisions are triggered when the LWC in the parcels exceeds a threshold value LWC threshold, which in the RF07 case turns out to be 1.5 g m 23.

21 APRIL 2009 M AGARITZ ET A L. 801 FIG. 22. The Z LWC diagram for simulation RF07. Each point indicates a cloud parcel. The location of parcels in the diagram are indicated every 5 min. Colors denote the height of parcel location in the BL. Lines indicate approximate dependencies of Z as a function of LWC for three regimes: (i) the diffusion growth, (ii) collision triggering, and (iii) the regime of the developed drizzle (see Part I for details). (ii) The LWC threshold value exceeds the maximum horizontally averaged LWC (of 0.8 g m 23 )by;two standard deviation values. The latter shows that the number of the parcels with LWC. LWC threshold (referred to as lucky parcels) in clouds with light drizzle is quite small: about 0.6% of the total number of cloudy parcels. In the nondrizzling RF01 case the fraction of parcels with 1.5 g m 23 was negligible both in observations and in the model simulations. We assume that for formation of heavy drizzling clouds the fraction of lucky parcels must be larger than 1%. (iii) The lucky parcels start their motion near the surface and reach the cloud top, where they remain for a comparatively long period of time. Their tracks are closely related to the outermost streamline of large eddies. Large droplets form first in the lucky parcels near the cloud top. This result following from the numerical analysis can be also derived from the observed data presented by Wood (2005) and vanzanten et al. (2005, their Fig. 2). (iv) Rapid drizzle formation starts in the parcels when effective radius exceeds mm, which is in agreement with observational (Gerber 1996; Yum and Hudson 2002; vanzanten et al. 2005; Twohy et al. 2005) and numerical (Pinsky and Khain 2002) results. FIG. 23. Horizontal cross sections of (a) drizzle flux at z m, (b) drizzle flux at z m, and (c) vertical velocity at z m in the RF07 run at t min when the maximum drizzle flux takes place. The zones of strong rain flux correspond to the zones of downdrafts.