The mechanism of drizzle formation in shallow stratocumulus clouds and the
effect of turbulent mixing on this process are investigated. A
Lagrangian–Eularian model of the cloud-topped boundary layer is used to
simulate the cloud measured during flight RF07 of the DYCOMS-II field
experiment. The model contains
Understanding the mechanism of drizzle formation in stratocumulus clouds (Sc) is a long-standing problem in cloud physics. Formation of drizzle in the cloud leads to changes in the radiative properties of Sc (Nakajima and King, 1990; Gerber, 1996; Feingold et al., 1999; Brenguier et al., 2000; Rosenfeld et al., 2006, 2012). Sc cover large areas of the globe and as a result microphysical processes occurring within them have a profound effect on global radiation balance. The problem of drizzle formation is also interesting from a theoretical point of view. In Sc, drizzle forms within narrow cloud layers of a few hundred meters, which contain only little liquid water compared to more developed cumulus. Studies have shown that both an increase in cloud depth (Pawlowska and Brenguier, 2003; Kostinski, 2008) and an increase in the drop residential time in the cloud (Feingold et al., 1996; Magaritz et al., 2009) foster drizzle formation.
Warm Sc were investigated numerically using Large Eddy Simulations (LES) with different levels of complexity to describe microphysical processes (Stevens et al., 2003b, 2005; Ackerman et al., 2009). Among these, LES models of Sc with spectral bin microphysics were used to parameterize the rates of auto-conversion and drizzle formation (Khairoutdinov and Kogan, 1999). These parameterizations are widely used in large-scale models (Randall et al., 2003). And still, many LES models fail to reproduce the observed structure of Sc. Specifically, LES tend to substantially underestimate values of liquid water content (LWC) near cloud top (Stevens et al., 2005). Stevens et al. (2005) attributed these results to uncertainties in the description of small-scale turbulent motion in LES models. That study concluded that a realistic structure of Sc can be simulated only if the LES has a spatial resolution as low as 1 m – i.e., in configurations in which most turbulent motions are described explicitly.
Pinsky et al. (2008) and Magaritz et al. (2009) described a new Sc model, referred to as a Lagrangian–Eulerian model (LEM). In the model several thousand adjacent parcels (Lagrangian) move within a turbulence-like flow, with statistical parameters measured in the Stratocumulus-Topped Boundary Layer (STBL). The initial model version (Pinsky et al., 2008; Magaritz et al., 2009) did not include turbulent mixing of adjacent parcels and did not consider the effects of mixing and entrainment at the upper cloud boundary. Nonetheless, the model successfully simulated many observed properties, such as LWC, droplet size distribution, and drizzle formation. It was found that drizzle forms initially in “lucky” parcels that ascend from the ocean surface and spend the most time near cloud top. Such lucky parcels were estimated to comprise about 1 % of all air parcels. The large droplets falling from “lucky” parcels trigger collisions and drizzle formation in parcels located below them. It was found that drizzle tends to fall in downdrafts created by large eddies in the STBL.
In the previous model version, consideration of a more realistic STBL geometry, characterized by a dry and warm inversion layer above the cloud top, led to the formation of an unrealistic cloud structure. The extremely inhomogeneous structure was caused by entrainment of dry and warm air volumes into the cloud layer. The radius of correlation of all microphysical variables became equal to parcel size selected in the model, which is much lower than the radii of correlation calculated from observed data.
In order to make cloud structure realistic and represent processes resulting
from interaction with the inversion layer, it was necessary to take into
account processes of entrainment and mixing of adjacent parcels
(Magaritz-Ronen et al., 2014). It was shown that turbulent mixing of parcels
leads to realistic spatial variability of microphysical quantities
characterized by a spatial correlation scale of
In the present paper we simulate a slightly drizzling cloud observed during research flight RF07 of the same field campaign. The study presented here addresses two questions. First, given that turbulent mixing limits the lifetime of separate cloud volumes, does the concept of “lucky” parcels as triggers of drizzle formation remain valid? Second, what is the role of mixing in this process? Especially, what is the effect of mixing of dry and warm air from the inversion on drizzle formation in the cloud? We also address the question of whether DSD broadening caused by mixing at the cloud top favors drizzle formation, or delays the process.
The model used in this study was first described in Pinsky et al. (2008) and Magaritz et al. (2009). It has been modified since the first studies were described in those papers. New processes such as surface fluxes, radiative cooling from cloud top, and most important, turbulent mixing of air parcels, have been incorporated. Some main model developments as were first presented in Magaritz-Ronen et al. (2014) are further described below.
The model contains about 2000 adjacent Lagrangian parcels with a
characteristic linear size of 40 m. The parcels cover the entire 2-D model
domain of
The velocity field is represented as the sum of a large number of harmonics
with random time-dependent amplitudes. The velocity field is assumed
quasi-stationary during the entire simulation, statistically uniform in the
horizontal direction, and obeys the Kolmogorov
Droplet growth by collisions is described using the stochastic equation for
collisions and 1
One of the most prominent features of this model is that parcels are not isolated and there are two types of interaction between Lagrangian parcels: droplet sedimentation and turbulent mixing. Droplet sedimentation through parcel boundaries allows larger droplets that form in cloud parcels to act as drop collectors during their fall and reach the surface as drizzle. To calculate sedimentation the entire computational area is covered by an auxiliary regular grid with a 5 m resolution. Droplet flux is calculated through each of 5 m grid increments separating adjacent parcels.
Turbulent mixing between adjacent Lagrangian parcels is described using an
expansion of
To calculate mixing of DSDs, droplet flux is calculated between parcels. Because DSDs are not conservative variables, the increase or decrease in droplet size during transport from one parcel to another is taken into account according to the equation of diffusion growth. Thus, mixing at sub-grid scales is accompanied by latent heat release. This process differs from latent heat release at the resolvable scales, where supersaturation is determined by the parcel's vertical motion and droplet concentration.
Since the parcels move within an Eulerian coordinate system and droplet sedimentation is performed at the regular Eulerian finite-difference grid, the model is regarded as a Lagrangian–Eulerian Model (LEM).
Sensible and latent heat surface flux is calculated using the
bulk-aerodynamic formulas, with a Dalton number of
Parameterization of long wave radiative cooling based on the two-stream approximation following Khvorostyanov (1995) and Khvorostyanov et al. (2003) is used in the model.
The model has periodic boundary conditions in the horizontal direction. There
is no averaged air subsidence above cloud top in the model. In the STBL
large-scale subsidence sharpens gradients of temperature and humidity at the
upper cloud boundary and can reduce the rate of increase of cloud top height.
In the model, the rate of mixing and entrainment at cloud top is determined
by the slope of the
For this study the cloud observed during flight RF07 of the DYCOMS-II field
campaign (Stevens et al., 2003a) was simulated in the model. The
Sc measured during this night flight was
Measurements of the vertical profile of
The dissipation rate of turbulent kinetic energy (
Initial aerosol distribution was derived from observations (total
concentration 200 cm
In this study we investigate the formation of the first large-sized drops and drizzle in shallow Sc and the role of turbulent mixing in this process. To this end several simulations were performed. The control run (CON) included all processes and simulated the cloud measured during flight RF07. Supplemental simulations included a simulation with no turbulent mixing between the parcels (NoMI), a simulation with no sedimentation between the parcels (NoSd), and a simulation without mixing and sedimentation (NoMIS). Measurements from flight RF07 of the DYCOMS-II field experiment were used for validation of the model results.
Fields of LWC in the CON and NoMI simulations plotted at
Turbulent mixing at cloud boundaries and inside the cloud layer has a strong effect on the macroscopic properties of the cloud and drizzle formation, especially homogenization of clouds in the horizontal direction, as discussed in detail by Magaritz-Ronen et al. (2014).
A snapshot of the field of LWC at
It is seen that in some parcels LWC exceeds 1 g m
In the NoMI case, the LWC field is highly inhomogeneous throughout the cloud, indicating a smaller radius of correlation of the order of the linear size of one parcel. Substantial inhomogeneity is also seen near cloud base, indicating a high variability in the LCL of separate parcels. One can see that in CON cloud is thicker than in NoMI, with higher cloud top and lower cloud base. This difference is the result of turbulent mixing between parcels.
Figure 2 compares the profiles of LWC, concentration, temperature, and total
humidity
Figure 3 shows the evolution of the median profile of the effective radius
Profiles of LWC, droplet concentration (
Changes in the effective radius median profile in the CON (top) and NoMI (bottom) simulations.
Examination of profiles of the median
The evolution of the
Larger values of
LWC vs. collision parameter scatter plot for all cloud parcels at 200–220 min of simulation in the CON case. Color denotes the height of the parcel.
Fields of different parameters plotted at
Several studies have shown that for the formation of large droplets in the
DSD, efficient collisions are crucial (Pinsky and Khain, 2002; Khain et al.,
2013). The rate of collisions can be characterized by the product of the
square of droplet concentration and collision kernel. This product represents
the gain integral in the stochastic equation of collisions (Pruppacher and
Klett, 1997). Evaluations of the collision kernel conducted by Freud and
Rosenfeld (2012) found that the kernel is proportional to
Figure 5 illustrates the mechanism of formation of parcels with maximum
values of LWC. This figure shows the field of humidity at
A previous study (Magaritz-Ronen et al., 2014) found that with turbulent
mixing the lifetime of a single 40 m parcel is of the order of
History of a single parcel marked in Fig. 6.
The process of lucky parcel formation is further illustrated in Fig. 6a. All
parcels located at the bottom of the domain, near sea surface at
Figure 7 presents the evolution of microphysical parameters of a single
parcel. This parcel, which is marked in Fig. 6a by black circles in all
panels, ascends from cloud base to 800 m in 13 min (panel b). The effective
radius in the parcel increases to 12
In Fig. 8 we examine only those parcels that reach a value of LWC greater
than 0.8 g m
Maximum collision parameter as a function of the accumulated time a
parcel has LWC
LWC vs.
The first large droplets form near cloud top, where mixing with dry environment is most pronounced. Inhomogeneous mixing is often suggested as a mechanism leading to increase in the maximum drop size in ascending cloud volumes mixing with the environmental in cumulus clouds (Baker et al., 1980; Baker and Latham, 1982; Lasher-Trapp et al., 2005; Cooper et al., 2013), it is therefore of interest to investigate the possibility that turbulent mixing at cloud top of Sc may accelerate the formation of these droplets.
Figure 9 shows a scatter diagram of droplet concentration and LWC (LWC–
LWC vs. spectrum width scatter diagrams for the CON (left) and NoMI
(right) cases. Each dot represents a parcel during 195–220 min of
simulation. In the top row
Figure 10 compares DSD widths (standard deviation of the distribution) as a function of LWC in simulations with (CON, panels a, c) and without mixing (NoMI, panels b, d). In the CON case the spectrum width values are higher than in the NoMI case. In CON, DSD width is maximal in zone 2, where mixing leads to the formation of small droplets and broadening of DSD. These parcels correspond to the parcels in zone 2 in Fig. 9, where the decrease in LWC is seen to be greater than the concentration. As mentioned above, partial evaporation of droplets in these parcels is the principal process leading to broadening of DSD toward smaller drops and increasing spectrum width. While spectrum width is greatest in parcels at cloud top, the strongest collisions are in the most adiabatic parcels with the largest LWC (zone 1). These parcels may have lower DSD width, because they contain fewer small droplets. In parcels that interact with the inversion air, mixing with dry environmental air increases spectrum width towards smaller drops and decreases the rate of collisions. If sufficiently large drops formed in the parcel before it mixed with the dry inversion air, collisions can still be efficient and drizzle-size drops may form.
In adiabatic parcels, the spectrum width is determined by a combination of
the initial spectrum at cloud base and the path of the parcel in the cloud.
The initial DSD is a function of the supersaturation at the LCL and the
aerosol distribution. Further ascent of the parcel is accompanied by
diffusion growth and, if conditions permit, the beginning of collisions and
widening of the DSD towards large drops. Variability of spectrum width values
increases when the parcels are not adiabatic (Fig. 10). In the case of
turbulent mixing, the width of an individual spectrum is not a direct result
of the parcel's history but also of the history of adjacent parcels. These
wider DSD may expedite drizzle formation in the cloud. But in general, we see
that the DSD width is not the main factor that fosters intense collisions and
in our case first drizzle drops. Diffusion growth leads to DSD narrowing in
the space of drop radius; in the space of
It is interesting to note that in addition to a higher collision parameter, LWC maximum values are greater in the CON case than in the NoMI case as well. These higher LWC values indicate a deeper cloud. During the simulation, sensible and latent heat fluxes from the surface increase the humidity in the boundary layer and lead to a decrease in cloud base height as was mentioned above. These changes result in an increase of the LWC max near cloud top.
Conclusions inferred from the previous figures regarding the shape of the DSD
are supported by Fig. 11, where DSDs at 100 m layers near cloud top are
presented. The DSDs are separated by LWC value and averaged in the horizontal
direction. For all presented DSDs the distribution peak is located at similar
radii. The concentration of drops around 10
Note that mixing between parcels in the model is inhomogeneous, because it takes significant time (15–20 min) for homogenization (according to homogeneous mixing homogenization is instantaneous). At the same time mixing leads to DSD broadening. This contrasts with the classical theory that assumes the shape of DSD to be unchangeable in the case of extreme inhomogeneous mixing. We attribute this difference to the simplifying assumption of monodisperse DSD in the classical mixing concepts.
In previous sections we discussed the properties of “lucky” parcels where first drizzle is formed. “Lucky” parcels have high absolute humidity. They originate from near the surface and reach the upper levels of the cloud quickly, not allowing sufficient time for mixing with the surrounding air. In these parcels collisions lead to the formation of drizzle followed by sedimentation of the largest drops.
Averaged DSD at three layers near cloud top. At each level DSD is averaged according to LWC value.
In this section we wish to observe the effects of turbulent mixing on the
formation of “lucky” parcels as well as on the further development of
drizzle in the cloud. Figure 12 compares the accumulated mass and accumulated
number of drops larger than 20
Accumulated mass
Large droplets first form in cases where drop sedimentation is removed. In these simulations drops become very large and grow by collisions to unrealistically large sizes, and yet they provide insight into the process of first drizzle drop formation.
In the NoMISD case the mass increases faster and earlier in the simulation
than in the NoSD case. When the parcels are adiabatic, parcels initially
located near the surface where humidity is maximal will have the lowest LCL
and maximum LWC. In the NoMISD these parcels retain their extreme values of
humidity and large drops form earlier. Inclusion of mixing between the
parcels leads to a reduction of maximum values, homogenization of the BL, and
a subsequent delay in the formation of large droplets (NoSd, left panel).
From these results it can be seen that the first large droplets will form in
adiabatic parcels with initially high humidity. The accumulated number of
large drops (right) further supports this conclusion. In NoMISD the number of
large drops increases until
When sedimentation is included in the simulations, after some drops become large enough they may fall through the cloud. In the NoMI case large drops forming in a small number of parcels sediment through the cloud and evaporate in other parcels, especially in dry and warm parcels penetrated from the inversion (Fig. 1). As a result, the amount of large droplets that form in the cloud remains very low and the mass of these large drops is negligible. This evaporation process prevents the formation of drizzle at the surface in the NoMI case. In CON simulation, when mixing is included, the cloud structure changes dramatically. As a result, droplets falling from parcels close to adiabatic do not evaporate but grow by collisions within the cloud. In this simulation drizzle develops and reaches the surface. After the initial formation of large drops in the most humid parcels in the cloud, the number of large drops in the CON case continues to increase, indicating that turbulent mixing facilitates the formation of drizzle in the cloud.
In general, Fig. 12 shows the two main phases of drizzle formation in Sc. First, larger droplets form in the most adiabatic parcels in the cloud layer. Second, turbulent mixing leads to further formation of more large droplets and drizzle-sized drops. In these two phases turbulent mixing plays a contradictory role, delaying the first while enhancing the second (see further detail in the discussion).
Averaged mass distribution for 100 m layers, plotted at
In the cloud's latter stages of drizzle development, large drops forming in
“lucky” parcels sediment through the cloud, leading to further development
of drizzle. In Fig. 3 this process is first seen as an increase of
Averaged rain flux at 450 m near cloud base, separated into downdraft (black) and updraft (gray) areas.
The dynamic structure of the BL and the presence of large eddies affect the continuation of drizzle development in Sc clouds as well. They determine areas of updraft and downdraft and are the controlling factor in the preferable trajectory of “lucky” parcels. As larger drops form along cloud top, droplets in parcels reaching areas of downdraft are more prone to sedimentation. Drizzle does not develop in the entire cloud simultaneously so that areas of more intense drizzle flux form. These areas coincide with downdraft areas in the cloud. Figure 14 presents the averaged rain flux near cloud base (450 m) throughout the simulation. Each bar shows the drizzle flux separated into downdraft and updraft areas. It can be seen that most of drizzle falls in these areas. Areas of enhanced drizzle were seen in observations of RF07 as well (Van Zanten et al., 2005).
In Fig. 14 it was shown that the mass and number concentration of larger drops increase when turbulent mixing is taken into account – far beyond those seen with no mixing. In addition to the inhibiting effect mixing has on the initiation of drizzle, turbulent mixing is needed for continued drizzle development in the cloud.
Among possible mechanisms able to lead to this effect we first consider changes to the aerosol size distribution. One of the specific features of the model used in this study is accounting for the aerosol distribution in each parcel. In addition to accounting for aerosols when the parcel is sub-saturated and all aerosols are in equilibrium with the environment, the model tracks aerosols in the drops themselves. Aerosol size does not change during processes of diffusion growth or evaporation, but in cases of collisions aerosol size grows and may reach larger sizes than initially found in the BL. Figure 15 presents the development through time of the maximum aerosol size in cloud parcels. The median profile of the maximum aerosol size in each parcel for the CON (top) and NoMI (bottom) cases is presented.
First, it is clear that the changes in the maximum aerosol size are very
different in the two cases. In the NoMI case, largest aerosols are present at
the beginning of the simulation. These aerosols have an average size of
1.3
Change in the median profile of the maximum aerosol size in cloud parcels in the CON (top) and NoMI (bottom) case.
As seen in the previous section, initial conditions are a governing factor in the formation of large drops when the parcels are adiabatic, and drop formation will be much more rapid without mixing than in the case of mixing.
As the development of the cloud progresses in the CON case the maximum
aerosol size increases and reaches an average of more than 3
Mixing between parcels gives rise to the recirculation of aerosols in the cloud. Collisions lead to the formation of increasingly large droplets and aerosols during the recirculation. As a result, the maximum size of aerosols at cloud base increases which fosters the formation of larger droplets at cloud base (large haze particles) and above in ascending parcels. We believe that the droplets formed on the largest aerosols contribute to the formation of the tail of largest droplets in lucky parcels shown in Fig. 7b. After initiation of drizzle in the cloud, enhanced collisions and formation of drizzle leads to a rapid increase in aerosol size as clearly shown in Fig. 15. Larger aerosols continue to circulate in the BL, fostering further drizzle formation at the drizzle stage of cloud evolution.
Spectral broadening and formation of the largest droplets in Sc due to
turbulent mixing during vertical recycling of cloud air is discussed in a
study by Korolev et al. (2013). In that study it is suggested that mixing of
the DSD of parcels ascending and descending in the cloud should lead to the
presence of larger droplets in the ascending branch of the cloud near cloud
base and result in more efficient collisions as the parcel ascends. The
results seen in Fig. 15 can also foster formation of larger droplets in
ascending parcels, during the course of diffusion growth and collisions. In
combination with the increased spectral width seen in Fig. 10 and the
increase in the median profile of
The process of drizzle formation in Sc is investigated using LEM, with an accurate description of microphysical processes. The new version of the model includes the process of mixing between parcels and surface flux of heat and moisture. Lightly drizzling stratocumulus clouds observed during flight RF07 of the DYCOMS-II field campaign were successfully simulated.
Clouds observed in flight RF07 were simulated by an earlier version of LEM, where there was no mixing between parcels and no inversion layer above cloud top (Magaritz et al., 2009). In that study the hypothesis that first drizzle forms in a small number of air volumes near cloud top in which LWC is maximal was expressed and justified. The consideration of a more realistic geometry of the STBL with an inversion layer required the implementation of turbulent mixing between the Lagrangian parcels. The question arose, whether the hypothesis of “lucky” parcels can also be justified under conditions of mixing. Results of the present study show that the hypothesis of “lucky parcels” remains valid also when turbulent mixing is taken into account.
It was further shown that mixing creates a realistic structure of stratocumulus clouds but does not prevent the appearance of nearly adiabatic LWC values at cloud top. Among these air volumes in the cloud “lucky” parcels are the most humid and have the highest LWC and the most intense collisions.
It is shown that without mixing taken into account drizzle cannot form in stratocumulus clouds. Maximum LWC values are not as high and large drops can form only in a smaller portion of the parcels that reach cloud top. Effective radius in the cloud is lower and its linear profile remains nearly constant throughout the lifetime of the cloud.
In conclusion, turbulent mixing plays a dual role in the process of drizzle formation. On the one hand, the formation of the first large drops in Sc is an adiabatic process in which turbulent mixing is an inhibiting factor. It reduces maximal values of humidity and delays the formation of the first drops. On the other hand, turbulent mixing leads to the creation of generally favorable background conditions and increased aerosol size within clouds, allowing drizzle growth and development during drop sedimentation. In addition, mixing leads to an increase in the drop size (haze size) at cloud base leading to faster formation of largest drops in the ascending nearly adiabatic cloud volumes.
This research was supported by the Israel Science Foundation (grant 1393/14), the Office of Science (BER), the US Department of Energy Award DE-SC0006788, and the Binational US–Israel Science Foundation (grant 2010446). The authors express their gratitude to A. Kostinski for ideas about the existence of lucky parcels, where first drizzle forms. Edited by: M. Petters