This paper investigates the relative importance of turbulence and
aerosol effects on the broadening of the droplet size distribution
(DSD) during the early stage of cloud and raindrop formation. A
parcel–DNS (direct numerical simulation) hybrid approach is developed
to seamlessly simulate the evolution of cloud droplets in an ascending
cloud parcel. The results show that turbulence and cloud condensation nuclei (CCN) hygroscopicity
are key to the efficient formation of large droplets. The ultragiant
aerosols can quickly form embryonic drizzle drops and thus determine
the onset time of autoconversion. However, due to their scarcity in
natural clouds, their contribution to the total mass of drizzle drops
is insignificant. In the meantime, turbulence sustains the formation
of large droplets by effectively accelerating the collisions of small
droplets. The DSD broadening through turbulent collisions is
significant and therefore yields a higher autoconversion rate compared
to that in a nonturbulent case. It is argued that the level of
autoconversion is heavily determined by turbulence intensity. This
paper also presents an in-cloud seeding scenario designed to
scrutinize the effect of aerosols in terms of number concentration and
size. It is found that seeding more aerosols leads to higher
competition for water vapor, reduces the mean droplet radius, and
therefore slows down the autoconversion rate. On the other hand,
increasing the seeding particle size can buffer such a negative
feedback. Despite the fact that the autoconversion rate is prominently altered
by turbulence and seeding, bulk variables such as liquid water content
(LWC) stays nearly identical among all cases. Additionally, the lowest
autoconversion rate is not co-located with the smallest mean droplet
radius. The finding indicates that the traditional Kessler-type or
Sundqvist-type autoconversion parameterizations, which depend on the
LWC or mean radius, cannot capture the drizzle formation
process very well. Properties related to the width or the shape of the DSD are
also needed, suggesting that the scheme of is
conceptually better. It is also suggested that a turbulence-dependent
relative-dispersion parameter should be considered.
Introduction
Aerosol–cloud–precipitation interactions represent one of the major
uncertainties in weather and climate prediction
. Current atmospheric models cannot resolve the
microphysical processes and thus rely on parameterizations to
represent those interactions. Studies show that model results of the
location and intensity of precipitation are sensitive to microphysics
schemes . For example,
showed that the autoconversion scheme is the
dominant factor to account for the difference in rain production, and
the uncertainty due to the choice of microphysical parameterizations
exceeds the effects of aerosols. No benchmark “truth” from either
measurements or modeling exists to gauge the performance of various
microphysics schemes. On the one hand, in situ measurements cannot
directly obtain the process rates, such as the rate of autoconversion
and accretion, which prevents such microphysical processes from being
accurately modeled . The community has to rely on
laboratory experiments, indirect observations, or theoretical models
to develop and validate microphysical schemes
e.g.,. On the other hand,
it is difficult to create laboratory facilities, such as cloud chambers, with environments that are scalable to real clouds. Furthermore, the effects of
chamber walls, such as the heat and moisture fluxes fed into the solid
wall and the droplet loss due to their contact with the wall, are
challenging to quantify with considerable uncertainties in the
measurements e.g.,.
In this study, we implement the idea of in-cloud seeding, i.e.,
seeding hygroscopic particles near the cloud base, to investigate the
effects of aerosols in droplet growth and rain formation. Hygroscopic
cloud seeding, owing to its potential effect of increasing rainfall,
has been conducted in research and operational contexts globally to
address the shortage of water resources in arid environments
e.g.,. The general concept of
hygroscopic cloud seeding for rain enhancement is that the introduction
of artificial cloud condensation nuclei (seeding particles) into warm
clouds can, on the one hand, suppress the activation of small natural
aerosols, and on the other hand, generate large initial particles that
accelerate or enhance the collision–coalescence process
. Regardless of its existence in operational weather
modification for decades, the direct effect of seeding is still
inconclusive (partly due to the chaotic nature of the convective cloud
system), making it impossible to conduct controllable seeding
experiments because of the limitation in detecting and assessing the seeding
results with current instrumentation . Nevertheless, the progress made in cloud seeding does
advance our understanding of cloud–aerosol–precipitation
interactions. A leading idea of this study is to make use of the
concept of cloud seeding experiments to separate the influence of
aerosols on rain initiation from the effects of natural cloud
processes such as turbulence and aerosol hygroscopicity, as well as to
shed light on the long-existing question of whether cloud seeding
could enhance precipitation.
Currently, direct numerical simulation (DNS) is believed to be the
only numerical approach capable of simulating the growth of individual
cloud particles in turbulent flows . Only a few
DNS studies to date investigated the evolution of the droplet size
distribution (DSD) in an updraft environment
e.g.,. However, the solute
effect (aerosol hygroscopicity) and curvature effect were excluded in
those works for simplicity. Parcel model studies on droplet
condensation in a lifted parcel show that the curvature term and the
solute term can lead to condensational broadening on the droplet size
spectrum. demonstrated that the curvature
effect is essential for DSD broadening in an ascending
parcel. found that the curvature effect and the
solute effect lead to irreversible broadening when supersaturation
fluctuations are present. It is also found that aerosols of different
sizes and different hygroscopicity can cause spectral broadening
without supersaturation fluctuations . Therefore, it is crucial to examine whether these effects
are important in spectral broadening when they dynamically couple with
droplet collisional growth in a turbulent environment.
It is recognized that DNS is computationally expensive. To achieve an
accurate representation of cloud microphysics while maintaining a
feasible computational load, a hybrid modeling framework that combines
a parcel model and a DNS model is proposed in this study. The parcel
model provides the mean state of the air parcel and can be used when
the effect of turbulence is less prominent. The DNS model explicitly
resolves all small-scale turbulent eddies which are key to cloud
particle interactions. The Lagrangian particle-by-particle method is
employed in the DNS to track the evolution of individual cloud
particles coupling with the turbulent flow. This hybrid parcel–DNS
approach allows for a close examination of the growth history of cloud
particles from aerosol activation to drizzle formation. By comparing
simulations with different aerosol and turbulent conditions, we are
able to evaluate the contribution of each microphysical component to
warm rain initiation. The ultimate goal is to provide a numerical
benchmarking tool to better understand aerosol–cloud–precipitation
interaction at fine scales and improve the subgrid-scale
representation of clouds and precipitation in numerical weather and
climate prediction.
found that the evolution of DSD in turbulence is
different depending on whether droplets grow by condensation-only,
collision-only, or condensation–collision (Fig. 1 in their
paper). This reveals that droplet condensation and collisions, when
interacting with turbulence, cannot be treated as the linear addition
of the two processes. Many past DNS studies focused on either the
condensation-only process or the collision-only process, which might
yield biased results. It should be pointed out that autoconversion
defined as the mass transfer from small droplets to embryonic drizzle
drops via collision–coalescence should not exclude the impact of
condensational growth, as the two processes dynamically interact with
each other.
This paper presents a sequel to the study of by
addressing several caveats mentioned in their paper. Firstly,
treated only pure-water droplets as is commonly
assumed in most DNS studies
e.g.,. This
simplification may underestimate the rate of droplet growth by
condensation. found that cloud condensation nuclei
(CCN) strongly enhance the particle growth, and droplets with giant
CCN can even grow in regions of subsaturated downdrafts. In our new
hybrid approach, we use an accurate droplet diffusional growth
equation including both curvature effect and solute effect. Secondly,
the initial DSD in obtained from flight observations
was a result of averages over a long time period and along a long
sampling path (including both core regions and cloud edges). The
average might mask the local property of an adiabatic core that the
DNS aims to simulate. The adiabatic cores are regions free of
entrainment of dry air. This region has a higher liquid water content
(LWC) than the rest of the cloud and is argued to favor the formation
of raindrops . To represent the DSD evolution at the
core region, we prescribe here a dry aerosol size distribution in the
subcloud region, and the aerosol activation process is explicitly
simulated by a parcel model to provide a more physically based initial
DSD for the DNS.
The main purpose of the present study is to investigate the relative
importance of turbulence, CCN hygroscopicity, and aerosols (size and
number concentration) on the DSD broadening in cumulus clouds. The
paper is organized as
follows. Section – introduce the
hybrid model of a parcel–DNS framework. In Sect. ,
the configuration of the 12 numerical simulations are described to
compare the microphysical responses to turbulence (turbulent vs.
nonturbulent), hygroscopicity (pure-water droplets vs.
solute-containing droplets), aerosol size and number concentration
(with or without seeding particles), and droplet growth mechanisms
(condensation-only vs. condensation–collision). Results are presented
in Sect. , showing that turbulence and CCN
hygroscopicity are key to the formation of big droplets, and seeding
slows down the broadening and lowers the autoconversion rate. The summary
and outlook for future work are in Sect. .
Model setup
A hybrid model is used in this paper for simulating the droplet growth
inside an ascending cloud parcel. The ascent is divided into two
phases based on the distinct dominant microphysical processes. A
parcel model and a DNS model are combined to seamlessly simulate the
two phases, as illustrated in the schematic diagram in
Fig. . The first phase starts from the unsaturated
subcloud region (≈300m below cloud base) to the
level where the supersaturation reaches a maximum (≈43m above cloud base; see Fig. a). During
this phase, supersaturation increases with height, and the
microphysical process is dominated by aerosol activation. Cloud
particles remain small and collisional growth is negligible. A
nonturbulent parcel model is employed to calculate the droplet growth
by condensation in this phase. The second phase starts from the level
of maximum supersaturation (=1.59%) to 1km above,
which takes 500 s in simulated time (Table ).
At this stage, no new activation occurs as the supersaturation starts
to decrease with height. This phase is dominated by cloud droplet
growth. The DNS model is employed to calculate individual droplet growth
by condensation and collision, and these droplets are affected by their immediate local
turbulent environment. The parcel model state at the height with maximum
supersaturation is fed into the DNS model as initial conditions. Because
unactivated aerosols have little influence on the subsequent droplet
growth or on the water vapor field, only the activated aerosols from
the parcel model are carried over to the DNS model as the initial
background aerosol condition to decrease the computational load. The
CCN size distribution and droplet size distribution are displayed in
Fig. c. This parcel–DNS hybrid model provides an
economical approach, and is the first step towards a fully DNS-resolved
simulation of the entire ascending process.
Schematic diagram of the parcel–DNS hybrid model along with the unscaled bulk supersaturation with height. The parcel model simulates the ascending process below the height of maximum supersaturation (dashed blue line), and the DNS simulates the subsequent ascending process (solid violet line).
(a) Supersaturation and (b) radius of droplets with different initial wet sizes varying with the height from cloud base (H-HCB). Only bins of activated particles are illustrated in (b). (c) The background natural CCN (dry particle) size distribution in the parcel model (light dotted blue histogram) and in the DNS model (darker solid blue histogram), as well as the droplet size distribution at maximum supersaturation (Smax=1.59%) in the parcel model (light dotted violet histogram) and in the DNS model (darker solid violet histogram). The vertical axis denotes the number concentration of the assigned particle size in the model.
Parcel model
The parcel model is adopted from with two main
modifications. (1) The droplet collision–coalescence is excluded for
simplicity, because most particles in this phase are smaller than
10 µm. These droplets have very low collision rates even
in strong turbulence , and the growth is
dominated by condensation. (2) The hygroscopicity parameter, κ,
proposed by their Eq. 6 is employed in the
droplet diffusional growth equation:
RdRdt=S-R3-Rd3R3-Rd3(1-κ)exp2σwRvρwTRρwRvTesD′+ρwLvK′TlvRvT-1fv,
where R is droplet radius, Rd is the radius of CCN, σw=7.2×10-2Jm-2 is surface tension of water against air,
Rv=467Jkg-1K is individual gas constant for water
vapor, ρw and ρa are the density of water and air,
respectively, T is air temperature, and es is the saturated water
vapor pressure. D′ and K′ are, respectively, the water
vapor diffusivity and thermal conductivity that include kinetic
effects see Eq. 11a–b in, and Lv=2.477×106Jkg-1 is the latent heat of
vaporization. S is supersaturation ratio defined as
qvqvs-1, where qv and qvs are
water vapor mixing ratios at the current conditions and at saturated
conditions, respectively. fv is the ventilation coefficient, which takes
into account the distortion in water vapor field around the droplet
surface when the droplet moves relative to the flow. Studies show that
the effect is negligible when droplets are smaller than 10µm in radius p. 116. Therefore, the ventilation
effect is excluded in this phase (i.e., fv=1). In DNS, we apply the
empirical formulas of fv from , which depend on
the droplet Reynolds number and Schmidt number see also
Eqs. B2–B3 in.
There are two advantages to using the hygroscopicity parameter. (1)
The chemical information of the aerosol (i.e., molecular weight, van 't Hoff factor, density, etc.) is simplified into a single parameter in
the solute term; (2) the hygroscopicity parameter of mixed solute due
to collision–coalescence can be simply calculated by a weighted
average of the volume fractions of each component in the mixture
.
The initial environmental conditions are taken from the cumulus cloud
case of Table 2. The parcel ascends from
H=600m (≈284m below cloud base) with a
constant updraft velocity of 2.0ms-1, resembling a
fair-weather cumulus cloud condition. The detailed information is
listed in Table . The CCN (dry aerosol) size
distribution fits a lognormal distribution, taken from the pristine
case by (light blue histogram in
Fig. c). The distribution consists of three
lognormal modes in which the geometric mean dry radii in the three
modes are R={0.0039,0.133,0.29}µm, the geometric
standard deviations are σ={4.5394,1.6218,2.4889}, and the
total number concentrations of the whole size range are
N={133,66.6,3.06}cm-3. The initial size is discretized
into 39 bins on a log scale with the bin width set by doubling the
mass or with a multiplication factor in radius of 2.0. In this way,
the resolution is higher at small particle sizes and lower at large
particle sizes. The bin size ranges from 0.006 and 49µm, which gives a total number concentration of
N=112cm-3. To examine the variation in the activation
fraction of the aerosols due to bin width resolution, we performed
a sensitivity test with the number of bins spanning from 32 to 253,
corresponding to a multiplication factor from 2.2 to 1.1. The result
shows that the variation caused by changing the bin resolution has a
decreasing trend with increasing resolution, with a maximum variation
of 2.3 % of the total aerosol number concentration in the
32-bin case. In particular, the 39-bin case has only
0.6cm-3 more aerosols activated than in the 253-bin
case.
It is worth noting that the number concentration of CCN larger than
10µm is below 10-4cm-3, corresponding
to less than one particle in the DNS domain (L=16.5cm). The
hygroscopicity parameter of all aerosols is assumed to be κ=0.47. The
moving-bin method or moving-size-grid method see discussion
in is applied to calculate the evolution of the DSD. For
aerosols with dry radius Rd≤1µm, the
initial wet radius is set to the size when the droplet is in
equilibrium at the given ambient humidity: dR/dt=0. For giant aerosols with Rd>1µm, the initial wet size is assumed to be twice the dry
volume (i.e., R=21/3Rd). As illustrated in
Fig. b, the droplets with initial radius below
1µm grow quickly by condensation between
20–40 m above the cloud base before the maximum
supersaturation is reached, and droplets larger than 1µm
grow slower, creating a narrow DSD near the cloud base.
Model description and initial conditions of the parcel model and the DNS model.
ParcelDNSModel description Domain size0D air parcel0.165m×0.165m×0.165mΔx–1.289×10-3mΔt10-4s3.15×10-5sMicrophysics treatmentMoving-bin methodLagrangian particle-by-particle methodInitial conditions Initial temperature284.3 K281.2 KInitial pressure938.5 hPa902.2 hPaInitial number concentration of natural background aerosols112cm-385cm-3Initial saturation ratio85.61%101.59%Updraft velocity2.0ms-12.0ms-1Simulated time300 s500 sDNS model
All DNS simulations are initialized with an identical mean state
listed in Table . A constant mean updraft speed of
2ms-1 is prescribed to lift the air parcel. The initial
mean-state variables for DNS are obtained from the parcel model output
at maximum supersaturation (S=1.59%). Above this altitude,
no further activation is expected in the parcel due to the decreasing
supersaturation. The inactivated aerosols, corresponding to the first
two bins of the light blue histogram in Fig. c, do
not influence the subsequent evolution of the DSD. Therefore, only the
activated aerosols from the parcel model are carried over to the DNS,
reducing the particle number concentration to
N=85cm-3. This treatment avoids the computation of
tracking the inactivated particles. In the parcel model, the droplet
size is calculated by using the moving-bin method. The dry radius of
each bin remains constant, and the wet radius grows by
condensation. To assign the initial droplet size and its dry radius in
the DNS, we regrouped the activated droplet bins into 15 droplet size
groups (R=2–16 µm) with an interval of 1µm. Their CCN sizes remain at the original values. Due to the
parallelization setup in the model, the initial number of each droplet
size group has to be an exact multiple of the number of processors in
the simulation (64 processors are used in the present
simulations). Therefore, a small difference in the resulting DSD
between the two models is expected, as shown in
Fig. c.
The DNS model in the present study was initially developed by
and has undergone a few modifications since
then . The model
employs two sets of equations: (1) the macroscopic equations to
calculate the base-state (bulk) variables and (2) the microscopic
equations to calculate the fluctuation of the variables affected by
the small-scale turbulence and the local droplet condensation. A
detailed description of the DNS model can be found in Sect. 2
and Appendix B of that paper.
Two modifications are made in the present study. First, we use
Eq. () to replace the simplified version of the droplet
growth equation in Eq. B1 of that paper where the
curvature term and the solute term are excluded. Second, droplets with
R<5µm are treated as non-inertial particles due to their
small Stokes number, i.e., their velocity is equal to the flow
velocity. The length of a time step is constrained by the inertial
response time of the smallest inertial particle see discussion
inon the length of the time step. The treatment above
avoids using too small a time step when small droplets are present. For
droplets between 5 and 40 µm, their motion is determined by
both the Stokes drag force and gravity; for droplets over
40µm, nonlinear drag force is considered see full
description below Eq. B10 in. Droplets over
50µm is size are treated as fallout and are removed from the
simulation.
DNS experimental design
Two sets of experiments are performed. Each set consists of 6 cases,
which gives 12 simulations in total. The first set of the experiments
includes both condensational and collisional growth of droplets and
will be referred to as the “condensation–collision” set. The second
set excludes the droplet collision and will be referred to as the
“condensation-only” set. The model setup for the two sets is the
same other than the difference mentioned above. The configuration of
the six cases is listed in Table . We focus on the
condensation–collision set in the Results section unless explicitly
specified, and the condensation-only set is for the purpose of
comparison to evaluate the influence by condensation and
collision–coalescence.
Model configuration of the six cases in each set of the experiment. Two sets of experiments are performed: set one includes both collision and condensation in the droplet growth and is referred to as the condensation–collision set; set two only considers droplet condensation and is referred to as the condensation-only set. This gives 12 cases in total. The natural DSD is taken from the parcel model output at S=1.59%. Monodisperse seeding is considered in seeded cases with CCN size (Rd) and initial droplet size (R) listed in the table.
Run CTL is the control run. Only one condition is changed in each of
the other five cases. Run CTL, Run NoTurb, and Run NoSolu use the same
initial DSD from the parcel model and are referred to as the
“natural” cases. Turbulence and solute effects are switched off in
Run NoTurb and Run NoSolu, respectively, to gauge the effects of
turbulence and CCN hygroscopicity on the DSD. When turbulence is
switched off, the background velocity fluctuation is set to
0ms-1. Therefore, particle motion is only affected by
the mean updraft and gravitational settling, and the supersaturation
fluctuation is only induced by droplet condensation and
evaporation. When the solute term is switched off (i.e., κ=0),
droplets consist of only pure water. Run Seed-1N1R, Run Seed-2N1R, and
Run Seed-1N2R are referred to as “seeded” cases, because an extra number
of monodisperse aerosols are introduced near the cloud base (at the
beginning of DNS). Two seeding sizes and two number concentrations are
considered, as described in Table . Unlike
traditional cloud seeding, the same hygroscopicity of κ=0.47 is
assumed for both the natural aerosols and the seeding particles. In
Run Seed-1N1R, we introduce seeding particles of dry radius
Rd=0.1µm, wet radius R=4µm,
and number concentration N=10cm-3. We double the seeding
particle number concentration in Run Seed-2N1R. In Run Seed-1N2R, the
dry size of the seeding particles increased 10-fold and the wet size
doubled relative to Run Seed-1N1R (see Table ). It
should be pointed out that the dissipation rate in cumulus clouds
tends to increase with height . For simplicity, the
eddy dissipation rate (ϵ) for all the turbulent cases is set
to be statistically stationary (ϵ=500cm2s-3). The advantage
of this idealized, simplified treatment is that the effect of
turbulence can be easily separated from aerosol effects. A dissipation
rate of 500cm2s-3 represents a strongly turbulent environment
in cumulus clouds to examine the upper bound of turbulent effects on
the DSD evolution.
ResultsNatural cases
We first compare the results of the natural cases (Run CTL, Run NoTurb,
and Run NoSolu) to examine the effect of turbulence and hygroscopicity
(solute) on the droplet evolution. Figure shows that
including solute and turbulence effectively broadens the DSD at
different times. With droplets containing no solute in Run NoSolu, the
DSD broadening is suppressed within the first 6 min. However,
the tail evolution quickly catches up and converges to that in Run CTL
afterwards. Meanwhile, switching off turbulence in Run NoTurb
suppresses the DSD broadening at a later time
(Fig. ). The tail of the spectrum in Run CTL (and Run
NoTurb) stays similar in the first 2 min and starts to differ by
a large amount afterwards.
Time evolution of the droplet size distribution in the condensation–collision set of experiments. The droplet number concentration (cm-3) is indicated by colors with its value shown in the color bar. The configuration of each experiment is listed in Table .
Turbulence effects on the DSD broadening are minor before
T=6min (Fig. a–b). Both Run CTL and Run NoTurb
produce a similar number of droplets over 25µm in size at
T=6min. The majority of this size group is grown from the
ultragiant aerosol with initial dry and wet sizes of
Rd=4.9µm and R=16µm, respectively. They
grow rapidly to 25µm by condensation within the first
2 min in Run CTL and Run NoTurb. However, droplets can hardly
reach beyond 30µm solely by condensation
(Fig. d–e). The tail over 30µm is mainly
formed by the subsequent collision–coalescence process. Once droplets
are over 25µm, gravitational collection becomes
effective, leading to a similar DSD tail with or without
turbulence. However, gravitational collection of droplets below
25µm in Run NoTurb is ineffective to sustain the
formation of large droplets. After T=6min, the tail of DSD
in Run NoTurb becomes quasistationary for droplets over
20µm in size (red and blue histograms in Fig. b)
due to negligible gravitational collisions. This can be illustrated by
a negligible collision frequency in Run NoTurb in
Fig. e. In contrast, a substantial number of
droplets >20µm are constantly formed in Run CTL after
T=2min through rapid turbulent collisions. Comparing to
collision frequency in Run NoTurb (Fig. b),
turbulence substantially enhances the collisional growth of droplets
of R<20µm. The total collisions in turbulent cases
increase by a factor of 20. It is also found that the turbulent
enhancement of collisions is strongest among droplet pairs of similar
sizes, i.e., with a radius ratio of r/R>0.8. Similar-sized
collisions increase by nearly a factor of 50 in turbulent cases,
contributing to over 80 % of the total collisions as opposed
to 34 % in Run NoTurb. This is because a nonturbulent
environment does not favor similar-sized collisions due to a similar
droplet settling speed. Turbulence, on the one hand, increases the
relative motion between droplets and on the other hand, induces a
stronger clustering of similar-sized droplets. The two effects jointly
strengthen the similar-sized collisions. The turbulent enhancement on
similar-sized collisions is then amplified by the condensational
process. also demonstrated that as the condensation
process reduces the DSD width and generates more similar-sized
droplets, turbulence enhances the similar-sized collision and thus
broadens the DSD.
Even though turbulence intensifies the collisional growth, the
modulation on the droplet condensation is found insignificant. The
DSDs in Run CTL and NoTurb in the condensation-only set are nearly
identical (Fig. d–e). This is because the
supersaturation fluctuations are weak in an adiabatic core
region. found that in a quasiadiabatic
environment both particle sedimentation and short-lived turbulent
coherent structure reduce the supersaturation fluctuation and decrease
the time that droplets are exposed to these fluctuations. We expect
that the turbulent-induced condensational broadening is more
significant at the cloud edge, where entrainment mixing induces a large
variation in supersaturation fluctuations.
Droplet size distributions (DSDs) at T=0min (grey), T=2min (green), T=6min (red), and T=8min (blue) of the natural cases (Run CTL, Run NoTurb, and Run NoSolu). The upper panels (a–c) are the DSD in the condensation–collision set of experiments, and the lower panels (d–f) are the DSD in the condensation-only set of experiments.
When the solute effect is absent in Run NoSolu, droplets can hardly reach
beyond 30µm before T=6min
(Fig. c) because of a lack of ultragiant aerosols
(Rd>4µm). Embryonic drizzle drops at the
early stage (T<6min) are formed from the fast growth of the
ultragiant aerosols as seen in both Run CTL and Run NoTurb. No
significant change is found to be in the mean droplet radius or the
relative dispersion between Run CTL and Run NoSolu
(Fig. d). Only a slightly lower collision
frequency in the droplet size group of R>20µm results
from a lack of ultragiant aerosols (see the green histograms in
Fig. ). This implies that the solute effect on
droplet condensation in DSD broadening is small for aerosols below
Rd<4µm. The ultragiant aerosols
(Rd=4.9µm in this study), due to their
scarcity, have a negligible contribution in shifting the mean radius
and relative dispersion (Fig. ). As shown in
Fig. c, an efficient broadening is triggered at T=6min, resulting in a similar DSD as in Run CTL at the end of
the simulation. It is shown that droplets between 20 and 30 µm are produced through turbulent collisions by the end of T=6min (Fig. c), causing a boost in collisions of
droplets over 20µm in size (Fig. d).
The time evolution of collision frequency in
Fig. shows that all five turbulent cases show a
similar trend in total collisional frequency, even though the trend at
the four size groups varies. The nonturbulent gravitational
collection process is very weak with the collision frequency lowered
by at least 1 order of magnitude in Run NoTurb. Still, a slightly
higher droplet number concentration at R>40µm is
observed in Run CTL and Run NoTurb than in Run NoSolu because of the
presence of ultragiant aerosols. At the same time, the collision
frequency of the four size groups in Run CTL and Run NoSolu are almost
identical. Even though the ultragiant aerosols are important in
forming early drizzle embryos, due to a low number concentration, they
do not sustain an efficient collection process.
Collision frequency (CF) varying with r/R in the condensation–collision set of experiments. r/R is the radius ratio between the small droplet and the large droplet of collided droplet pairs. The droplet pairs are divided into four size groups by the big droplet radius, R, shown in the legend.
(a–d) Time evolution of collision frequency for droplet pairs of four different size groups mentioned in Fig. . (e) Time evolution of collision frequency for all droplet pairs.
The relative dispersion, defined as the ratio between the standard
deviation of the DSD and the mean droplet radius, is an indicator of
the width of the DSD. The values among the six cases at the end of the
simulation range from 0.01 to 0.1, which is highly consistent with the
theoretical study by Fig. 1 for an aerosol number
concentration close to 100cm-3. The dashed lines in
Fig. c demonstrate that condensational growth
narrows the DSD and decreases the relative dispersion throughout the
simulation in the condensation-only set. Droplet growth in the first
2 min is prevailed by condensation, as the relative dispersions
in the condensation–collision set of experiments well overlaps with
that in the condensation-only set. After T=2min the
relative dispersion in the condensation–collision set and the
condensation-only set start to deviate from one another. This is
mainly due to two factors: (1) the condensation narrowing slows down
as droplets get larger and supersaturation gets lower; (2) the
collision rate increases with the increasing droplet mean radius and
thus leads to a higher collision rate to strengthen the DSD
broadening. In Run NoTurb, the collision rate stays the lowest of all
cases throughout the simulation (Fig. e),
leading to the smallest relative dispersion of all six cases.
The temporal variation of bulk (a) liquid water content (LWC), (b) maximum droplet radius (Rmax), (c) relative dispersion, (d) droplet mean radius, (e) supersaturation ratio, and (f) autoconversion rate in the condensation–collision set of experiments (solid lines) and in the condensation-only set of experiments (dotted lines). The relative dispersion is defined as the standard deviation of the droplet radius divided by the mean radius. The autoconversion rate here is defined as the mass transfer rate from droplets smaller than R=30µm to droplets larger than 30µm. The droplets over 50µm in size are treated as fallouts and removed from the domain. Thus (b) only shows a maximum droplet size at 50µm.
Despite the fact that DSDs differ among the six cases, the modulation of the
bulk condensation by both turbulence and aerosol is negligible, as
supported by an almost identical LWC of the six cases
(Fig. a). This is because the fallout mass of
drizzle drops of R>50µm before T=500s is
negligible, and the bulk LWC of the six cases is approximately
adiabatic. Turbulence and aerosols redistribute water mass among
different droplet sizes by modifying the condensational and
collisional growth of individual droplets, thus shifting the droplet
statistics such as the mean radius and relative dispersion, and
eventually alter the autoconversion rate
(Fig. f). The autoconversion rate here is defined
as the mass transfer rate from droplets smaller than R=30µm to droplets larger than 30µm. It is also found that
even though Run NoTurb produces the second largest mean radius, the
autoconversion rate stays the lowest, which is accompanied by the smallest
relative dispersion. Therefore, properties such as the shape of the
DSD and relative dispersion are more relevant to autoconversion than
the LWC. The traditional autoconversion parameterizations such as the
Kessler-type parameterization and the
Sundqvist-type parameterizations
customarily use a threshold function based on the mean radius and/or
the LWC. It is suggested that autoconversion rate is also influenced
by various other parameters seeand references
therein. The present study demonstrates that both
parameters, in particular the LWC, cannot properly capture the trend
of the autoconversion. The autoconversion rate by ,
and its modified versions which include both the mean droplet size and
dispersion parameter, is conceptually better than the Kessler-type
schemes. Our results thus agree with , who found
that the scheme of is more sophisticated and
requires less tuning to match the observed onset of rain and
proportions of cloud and rain. They also found that the growth rate of
rain mass and number concentration are highly sensitive to the shape
and dispersion parameters. Additionally, it is worth noting that
turbulence modifies the collision rate and thus shifts the DSD shape
and relative dispersion. Therefore, a turbulence-dependent
relative-dispersion parameter is needed in developing the
autoconversion scheme.
Seeded cases
Seeding reduces the mean droplet radius due to higher competition for
water vapor among individual droplets
(Fig. d). Therefore, seeding slows down the
autoconversion process. Nevertheless, the LWC is not affected by
seeding (Fig. a), which again indicates that the
LWC is not a well-related quantity to autoconversion in this case.
When investigating the relative importance of aerosol and turbulence
to droplet growth, it is found that the modulation of droplet mean
radius by seeding particles is larger than the modulation by
collision–coalescence. In Fig. d, the difference
between seeded and unseeded cases exceeds the difference between the
condensation-only set (dotted lines) and condensation–collision set
(solid lines) of each case. Regardless, turbulent
collision–coalescence yields large droplets over 30µm
and increases the width of the DSD. The total collision rate is
heavily determined by the turbulence level and mildly affected by
seeding or CCN hygroscopicity (Fig. e). Besides,
the change in Rmax and relative dispersion due to
collisions exceeds that from changing the aerosol condition. As
condensational growth can hardly produce droplets over 30µm, turbulent enhancement of collision is determinant in the mass
conversion from small droplets to drizzle embryos. Meanwhile, seeding
increases the competition for water vapor among droplets and reduces
the mean droplet size, leading to more collisions of small droplets
and fewer collisions of large droplets
(Fig. a–d). Specifically, by doubling the
seeding particle number in Run Seed-2N1R, the condensational growth of
small droplets is further inhibited due to a higher competition of
water vapor, resulting in more small droplets. Increasing the size of
seeding particles in Run Seed-1N2R buffers the abovementioned
inhibition effect caused by increasing aerosol number
concentration. The resulting autoconversion rate ordering is Run
CTL > Run Seed-1N2R > Run Seed-1N1R > Run Seed-2N1R.
Finally, aerosol hygroscopicity is key to the onset time of
autoconversion. All five solute-containing cases see a similar onset
time around T=4min. Removing the solute (hygroscopic
material) in Run NoSolu delays the onset of autoconversion by about
1.5 min (green line Fig. f). Nevertheless,
after T=6–7 min, the autoconversion rate in Run NoSolu
exceeds all seeded cases. First, solute (CCN hygroscopicity) has a
negligible effect on the growth of small aerosols, as the size
distribution of small droplets in Run CTL and Run NoSolu remain almost
identical. This is substantiated by the almost identical collision
frequency of droplets below 20µm of the two cases
(Fig. a–c). Second, seeding reduces the mean
radius of the droplets. This leads to a reduction in collisions for
droplets over 20µm (Fig. d) and
subsequently decelerates the autoconversion process. The above
findings imply that increasing the aerosol size (ultragiant aerosol)
shortens the lifetime of the clouds through a fast onset of rain. And
increasing the number of aerosols decelerates the rain process.
Summary and discussion
This paper investigates the effects of turbulence and aerosol
properties (hygroscopicity, number concentration, and size) on the
microphysics during early cloud and rain development. A parcel–DNS
hybrid modeling framework is developed. The parcel model is used to
generate the initial size distribution of activated aerosols, and the
DNS model calculates the subsequent growth of those activated aerosols
affected by both the microscopic (turbulent fluctuation) and the
macroscopic (bulk) environment. By using this economical modeling
framework, continuous particle growth from subcloud aerosols to cloud
droplets is accurately represented.
Overall, ultragiant aerosols in the natural cases quickly form the
drizzle embryo and thus determine the onset time of
autoconversion. However, they only form a few big raindrops due to
their scarcity, which has little impact on the level of
autoconversion. Turbulence enhances the collision frequency by more
than 1 order of magnitude and determines the level of
autoconversion. Specifically, turbulence enhances the collisions among
similar-sized droplets that are less likely to happen in a
nonturbulent environment, effectively broadening the DSD. Therefore,
the autoconversion in a turbulent environment is significantly greater
than in a nonturbulent environment. It is also found that seeding
(increasing aerosol number and size) modifies the level of
autoconversion. On the one hand, increasing the aerosol number reduces
the mean radius due to stronger competition for water vapor, and
therefore slows down the autoconversion. On the other hand, increasing
the seeding size can buffer such a negative feedback. However, the
seeding of particles in this study only covers a limited range of dry
radius (R=0.1, 1 µm) and number concentration (N=10, 20 cm-3, corresponding to a 10 %–20 % increase in the total
number concentration). Conditions with more ultragiant aerosols (R≫1µm), lower aerosol concentrations (N≪100cm-3), or highly polluted environment (N≫100cm-3) will be of interest to further assess the
relative importance of aerosols and turbulence. It is argued that
predicting the rain onset time requires accurate information and
representation of ultragiant aerosols. And an accurate autoconversion
scheme requires a well-quantified turbulent collisions kernel.
Even though the autoconversion rate differs among the six cases, it is
found that the bulk variables such as LWC, mean radius, and
supersaturation are not sensitive to turbulence level and aerosol
conditions. In this case the LWC and mean droplet radius, which are
key parameters in Kessler-type or Sundqvist-type autoconversion
parameterizations, are not well-related quantities to autoconversion
rate, and information on turbulence intensity and aerosols is
essential to determine the autoconversion rate. It is argued that
these bulk variables are mainly affected by the updraft speed, which is
held the same among the six cases. Sensitivity studies are needed in
the future to investigate the effect of the LWC on the autoconversion
rate due to a change in the updraft.
Cloud models are sensitive to microphysics schemes, and the
autoconversion parameterization is one of the main sources of
uncertainty in the representation of warm clouds and rain with few
observations to verify against. The large uncertainty may be ascribed
to the decoupling of microphysics from subgrid-scale turbulence and a
lack of aerosol information in the parameterization. Therefore, the
aerosol effect evaluated by the models should be cautiously
interpreted. The hybrid parcel–DNS model can be used for verifying the
autoconversion rate affected by turbulence and aerosols at the
subgrid scale of large-eddy simulation (LES).
Despite a good number of improvements made, the current modeling
framework still presents the following shortcomings. For simplicity,
the same hygroscopic parameter (κ=0.47) is assumed among the
natural aerosols and the seeding particles. Besides, seeding is
initialized 40m above the cloud base, while traditional
hygroscopic seeding introduces particles around 100–300 m
below the cloud base. This treatment might affect the model results as
seeding below the cloud base influences the activation and growth of
the background aerosols and thus modifies the DSD at the cloud base
.
Our idealized simulations focus on the cloud adiabatic core region and
therefore exclude entrainment mixing, which is highly active near the
cloud edge. Activation of laterally entrained aerosols might occur in
cumulus clouds outside the adiabatic core
. The newly activated aerosols might
lead to a further broadening of the DSD e.g.,. In addition, the in-cloud mixing at a much larger
scale than the DNS domain transports and mixes both the air and
droplets from different parts of the cloud, including the cloud edge,
leading to a highly perturbed Lagrangian history of supersaturation
experienced by droplets “eddy hopping
effect”. On the other hand, larger turbulent eddies
can generate higher supersaturation fluctuations due to a higher
variation in a vertical motion and thus may both affect the aerosol
activation and broaden the DSD. Traditional DNS, which is confined to a
relatively small domain size (<1m), and the impact of
supersaturation fluctuations are significantly restricted. Methods such
as an upscaled DNS with superdroplets e.g., or
representing large-scale mixing with an external forcing on the
thermodynamic fields can be used for studying the
impact of turbulent scales on the supersaturation fluctuations and
thus on the condensational broadening of DSD. In conclusion, the
relative importance of entrainment, eddy hopping effect, small-scale
turbulence, and aerosols requires further investigation.
This study proposes the first DNS model framework for scrutinizing the
microphysical impact of cloud seeding and presents the first results
of such a model. Full DNS modeling from below the cloud base will be
the next step to include the effect of turbulence on aerosol
activation. Additionally, more realistic scenarios resembling actual
hygroscopic seeding conditions – such as utilizing multi-dispersive size
distributions, different hygroscopicity parameters, and seeding below
the cloud base – will be designed in the future development and
deployment of this framework.
Code and data availability
The data produced by the direct numerical simulation (DNS) model and parcel model can be accessed in the Harvard Dataverse repository 10.7910/DVN/HBIKKV. The parcel model and DNS model used to produce the dataset are available upon request.
Author contributions
This study was co-designed by SC, LX, and MKY. SC conducted the model simulation, did the data analysis, and wrote the article. LX and MKY provided advice and discussions on the model results and revised the article.
Competing interests
The authors declare that they have no conflict of interest.
Disclaimer
The work is original and has not been formally published before. It is also not under consideration for publication elsewhere.
Acknowledgements
We thank the two anonymous reviewers for their invaluable comments. We would like to acknowledge high-performance computing (HPC) support from Cheyenne, Graham, and Cedar. HPC resources at Cheyenne (10.5065/D6RX99HX) are provided by NCAR's Computational and Information Systems Laboratory and sponsored by the US National Science Foundation. HPC resources at Graham and Cedar are provided by Compute Canada (http://www.computecanada.ca, last access: 6 April 2020).
Financial support
This research has been supported by the Advanced Study Program at National Center for Atmospheric Research, sponsored by the US National Science Foundation (grant no. 1852977). Part of this work has been supported by the National Center of Meteorology, Abu Dhabi, UAE (UAE Research Program for Rain Enhancement Science).
Review statement
This paper was edited by Corinna Hoose and reviewed by two anonymous referees.
ReferencesBeard, K. V. and Pruppacher, H. R.: A Wind Tunnel Investigation of the Rate of
Evaporation of Small Water Drops Falling at Terminal Velocity in Air, J.
Atmos. Sci., 28, 1455–1464,
10.1175/1520-0469(1971)028<1455:awtiot>2.0.co;2, 1971.Berry, E. X. and Reinhardt, R. L.: An Analysis of Cloud Drop Growth by
Collection Part II. Single Initial Distributions, J. Atmos. Sci., 31,
1825–1831, 10.1175/1520-0469(1974)031<1825:aaocdg>2.0.co;2, 1974.Çelik, F. and Marwitz, J. D.: Droplet Spectra Broadening by Ripening
Process. Part I: Roles of Curvature and Salinity of Cloud Droplets, J. Atmos. Sci., 56, 3091–3105,
10.1175/1520-0469(1999)056<3091:dsbbrp>2.0.co;2, 1999.Chen, S., Bartello, P., Yau, M. K., Vaillancourt, P. A., and Zwijsen, K.: Cloud
Droplet Collisions in Turbulent Environment: Collision Statistics and
Parameterization, J. Atmos. Sci., 73, 621–636,
10.1175/JAS-D-15-0203.1, 2016.Chen, S., Yau, M. K., and Bartello, P.: Turbulence Effects of Collision
Efficiency and Broadening of Droplet Size Distribution in Cumulus Clouds, J.
Atmos. Sci., 75, 203–217, 10.1175/JAS-D-17-0123.1, 2018a.Chen, S., Yau, M.-K., Bartello, P., and Xue, L.: Bridging the condensation–collision size gap: a direct numerical simulation of continuous droplet growth in turbulent clouds, Atmos. Chem. Phys., 18, 7251–7262, 10.5194/acp-18-7251-2018, 2018b.Chen, S., Xue, L., and Yau, M.: Data support for “Impact of CCN
hygroscopicity and turbulence on cloud droplet growth: An in-cloud seeding
case study using parcel-DNS approach”, Harvard Dataverse, 10.7910/DVN/HBIKKV, 2019.Cooper, W. A., Bruintjes, R. T., and Mather, G. K.: Calculations Pertaining to
Hygroscopic Seeding with Flares, J. Appl. Meteorol., 36, 1449–1469,
10.1175/1520-0450(1997)036<1449:cpthsw>2.0.co;2, 1997.Fan, J., Wang, Y., Rosenfeld, D., and Liu, X.: Review of Aerosol–Cloud
Interactions: Mechanisms, Significance, and Challenges, J. Atmos. Sci., 73,
4221–4252, 10.1175/JAS-D-16-0037.1, 2016.Flossmann, A. I., Manton, M., Abshaev, A., Bruintjes, R., Murakami, M.,
Prabhakaran, T., and Yao, Z.: Review of Advances in Precipitation Enhancement
Research, B. Am. Meteorol. Soc., 100, 1465–1480,
10.1175/bams-d-18-0160.1, 2019.Franklin, C. N., Vaillancourt, P. A., Yau, M. K., and Bartello, P.: Collision
Rates of Cloud Droplets in Turbulent Flow, J. Atmos. Sci., 62, 2451–2466,
10.1175/jas3493.1, 2005.Gilmore, M. S. and Straka, J. M.: The Berry and Reinhardt Autoconversion
Parameterization: A Digest, J. Appl. Meteorol. Clim., 47, 375–396,
10.1175/2007jamc1573.1, 2008.Gotoh, T., Suehiro, T., and Saito, I.: Continuous growth of cloud droplets in
cumulus cloud, New J. Phys., 18, 043042,
10.1088/1367-2630/18/4/043042, 2016.Grabowski, W. W. and Abade, G. C.: Broadening of Cloud Droplet Spectra through
Eddy Hopping: Turbulent Adiabatic Parcel Simulations, J. Atmos. Sci., 74, 1485–1493, 10.1175/jas-d-17-0043.1, 2017.Grabowski, W. W., Andrejczuk, M., and Wang, L.-P.: Droplet growth in a bin
warm-rain scheme with Twomey CCN activation, Atmos. Res., 99, 290–301,
10.1016/j.atmosres.2010.10.020, 2011.Grabowski, W. W., Morrison, H., Shima, S.-I., Abade, G. C., Dziekan, P., and
Pawlowska, H.: Modeling of Cloud Microphysics: Can We Do Better?, B. Am.
Meteorol. Soc., 100, 655–672, 10.1175/BAMS-D-18-0005.1, 2019.Hoffmann, F., Raasch, S., and Noh, Y.: Entrainment of aerosols and their
activation in a shallow cumulus cloud studied with a coupled
LCM–LES approach, Atmos. Res., 156, 43–57,
10.1016/j.atmosres.2014.12.008, 2015.Jensen, J. B. and Nugent, A. D.: Condensational Growth of Drops Formed on Giant
Sea-Salt Aerosol Particles, J. Atmos. Sci., 74, 679–697,
10.1175/jas-d-15-0370.1, 2017.Kessler, E.: On the Distribution and Continuity of Water Substance in
Atmospheric Circulations, in: On the Distribution and Continuity of Water
Substance in Atmospheric Circulations, American Meteorological
Society, 1–84, 10.1007/978-1-935704-36-2_1, 1969.Khain, A., Prabha, T. V., Benmoshe, N., Pandithurai, G., and Ovchinnikov, M.:
The mechanism of first raindrops formation in deep convective clouds, J.
Geophys. Res.-Atmos., 118, 9123–9140,
10.1002/jgrd.50641, 2013.Korolev, A. V.: The Influence of Supersaturation Fluctuations on Droplet Size
Spectra Formation, J. Atmos. Sci., 52, 3620–3634,
10.1175/1520-0469(1995)052<3620:tiosfo>2.0.co;2, 1995.Lasher-Trapp, S. G., Cooper, W. A., and Blyth, A. M.: Broadening of droplet
size distributions from entrainment and mixing in a cumulus cloud, Q.
J. Roy. Meteor. Soc., 131, 195–220,
10.1256/qj.03.199, 2005.Liu, Y. and Daum, P. H.: Parameterization of the Autoconversion Process.Part I:
Analytical Formulation of the Kessler-Type Parameterizations, J. Atmos. Sci.,
61, 1539–1548, 10.1175/1520-0469(2004)061<1539:potapi>2.0.co;2, 2004.Liu, Y., Daum, P. H., McGraw, R., and Wood, R.: Parameterization of the
Autoconversion Process. Part II: Generalization of Sundqvist-Type
Parameterizations, J. Atmos. Sci., 63, 1103–1109, 10.1175/jas3675.1,
2006a.Liu, Y., Daum, P. H., and Yum, S. S.: Analytical expression for the relative
dispersion of the cloud droplet size distribution, Geophys. Res.
Lett., 33, L02810, 10.1029/2005gl024052, 2006b.Morrison, H., Lier-Walqui, M., Fridlind, A. M., Grabowski, W. W., Harrington,
J. Y., Hoose, C., Korolev, A., Kumjian, M. R., Milbrandt, J. A., Pawlowska,
H., Posselt, D. J., Prat, O. P., Reimel, K. J., Shima, S.-I., Diedenhoven,
B., and Xue, L.: Confronting the challenge of modeling cloud and
precipitation microphysics, J. Adv. Model. Earth Sy., 12, L02810,
10.1029/2019ms001689, 2020.Noh, Y., Oh, D., Hoffmann, F., and Raasch, S.: A Cloud Microphysics
Parameterization for Shallow Cumulus Clouds Based on Lagrangian Cloud Model
Simulations, J. Atmos. Sci., 75, 4031–4047,
10.1175/jas-d-18-0080.1, 2018.Paoli, R. and Shariff, K.: Turbulent Condensation of Droplets: Direct
Simulation and a Stochastic Model, J. Atmos. Sci., 66, 723–740,
10.1175/2008JAS2734.1, 2009.Petters, M. D. and Kreidenweis, S. M.: A single parameter representation of hygroscopic growth and cloud condensation nucleus activity, Atmos. Chem. Phys., 7, 1961–1971, 10.5194/acp-7-1961-2007, 2007.
Rogers, R. R. and Yau, M. K.: A Short Course in Cloud Physics, 3rd edn.,
Butterworth-Heinemann, Oxford, United Kingdom, 1989.Saito, I. and Gotoh, T.: Turbulence and cloud droplets in cumulus clouds, New
J. Phys., 20, 023001, 10.1088/1367-2630/aaa229, 2018.Sardina, G., Picano, F., Brandt, L., and Caballero, R.: Continuous Growth of
Droplet Size Variance due to Condensation in Turbulent Clouds, Phys. Rev.
Lett., 115, 184501, 10.1103/PhysRevLett.115.184501, 2015.Seifert, A., Nuijens, L., and Stevens, B.: Turbulence effects on warm-rain
autoconversion in precipitating shallow convection, Q. J.
Roy. Meteor. Soc., 136, 1753–1762, 10.1002/qj.684, 2010.Silverman, B. A.: A Critical Assessment of Hygroscopic Seeding of Convective
Clouds for Rainfall Enhancement, B. Am. Meteor.
Soc., 84, 1219–1230, 10.1175/bams-84-9-1219, 2003.Silverman, B. A. and Sukarnjanaset, W.: Results of the Thailand Warm-Cloud
Hygroscopic Particle Seeding Experiment, J. Appl. Meteorol., 39,
1160–1175, 10.1175/1520-0450(2000)039<1160:rottwc>2.0.co;2, 2000.Slawinska, J., Grabowski, W. W., Pawlowska, H., and Morrison, H.: Droplet
Activation and Mixing in Large-Eddy Simulation of a Shallow Cumulus Field,
J. Atmos. Sci., 69, 444–462,
10.1175/jas-d-11-054.1, 2012.Srivastava, R. C.: Growth of Cloud Drops by Condensation: Effect of Surface
Tension on the Dispersion of Drop Sizes, J. Atmos. Sci.,
48, 1596–1599, 10.1175/1520-0469(1991)048<1596:gocdbc>2.0.co;2, 1991.Stoelinga, M. T., Hobbs, P. V., Mass, C. F., Locatelli, J. D., Colle, B. A.,
Houze, R. A., Rangno, A. L., Bond, N. A., Smull, B. F., Rasmussen, R. M.,
Thompson, G., and Colman, B. R.: Improvement of Microphysical
Parameterization through Observational Verification Experiment, B. Am.
Meteorol. Soc., 84, 1807–1826, 10.1175/BAMS-84-12-1807, 2003.Sundqvist, H.: A parameterization scheme for non-convective condensation
including prediction of cloud water content, Q. J. Roy. Meteor. Soc., 104,
677–690, 10.1002/qj.49710444110, 1978.Terblanche, D. E., Steffens, F. E., Fletcher, L., Mittermaier, M. P., and
Parsons, R. C.: Toward the Operational Application of Hygroscopic Flares for
Rainfall Enhancement in South Africa, J. Appl. Meteorol., 39,
1811–1821, 10.1175/1520-0450(2001)039<1811:ttoaoh>2.0.co;2, 2000.Thomas, L., Grabowski, W. W., and Kumar, B.: Diffusional growth of cloud
droplets in homogeneous isotropic turbulence: DNS, scaled-up DNS, and
stochastic model, Atmos. Chem. Phys., 20, 9087–9100,
10.5194/acp-20-9087-2020, 2020.Thomas, S., Ovchinnikov, M., Yang, F., Voort, D., Cantrell, W., Krueger, S. K.,
and Shaw, R. A.: Scaling of an Atmospheric Model to Simulate Turbulence and
Cloud Microphysics in the Pi Chamber, J. Adv. Model. Earth Sy., 11,
1981–1994, 10.1029/2019ms001670, 2019.
Vaillancourt, P. A., Yau, M. K., and Grabowski, W. W.: Microscopic Approach to
Cloud Droplet Growth by Condensation. Part I: Model Description and Results
without Turbulence, J. Atmos. Sci., 58, 1945–1964,
10.1175/1520-0469(2001)058<1945:MATCDG>2.0.CO;2, 2001.Vaillancourt, P. A., Yau, M. K., Bartello, P., and Grabowski, W. W.:
Microscopic Approach to Cloud Droplet Growth by Condensation. Part II:
Turbulence, Clustering, and Condensational Growth, J. Atmos. Sci., 59,
3421–3435, 10.1175/1520-0469(2002)059<3421:MATCDG>2.0.CO;2, 2002.Wang, L.-P., Ayala, O., Kasprzak, S. E., and Grabowski, W. W.: Theoretical
Formulation of Collision Rate and Collision Efficiency of Hydrodynamically
Interacting Cloud Droplets in Turbulent Atmosphere, J. Atmos. Sci., 62,
2433–2450, 10.1175/JAS3492.1, 2005.White, B., Gryspeerdt, E., Stier, P., Morrison, H., Thompson, G., and Kipling, Z.: Uncertainty from the choice of microphysics scheme in
convection-permitting models significantly exceeds aerosol effects,
Atmos. Chem. Phys., 17, 12145–12175, 10.5194/acp-17-12145-2017,
2017.Wood, R., Field, P., and Cotton, W.: Autoconversion rate bias in stratiform
boundary layer cloud parameterizations, Atmos. Res., 65, 109–128,
10.1016/s0169-8095(02)00071-6, 2002.Xue, L., Teller, A., Rasmussen, R., Geresdi, I., and Pan, Z.: Effects of
Aerosol Solubility and Regeneration on Warm-Phase Orographic Clouds and
Precipitation Simulated by a Detailed Bin Microphysical Scheme, J. Atmos.
Sci., 67, 3336–3354, 10.1175/2010jas3511.1, 2010.Xue, L., Fan, J., Lebo, Z. J., Wu, W., Morrison, H., Grabowski, W. W., Chu, X.,
Geresdi, I., North, K., Stenz, R., Gao, Y., Lou, X., Bansemer, A.,
Heymsfield, A. J., McFarquhar, G. M., and Rasmussen, R. M.: Idealized
Simulations of a Squall Line from the MC3E Field Campaign Applying Three Bin
Microphysics Schemes: Dynamic and Thermodynamic Structure, Mon. Weather Rev.,
145, 4789–4812, 10.1175/MWR-D-16-0385.1, 2017.Yang, F., Kollias, P., Shaw, R. A., and Vogelmann, A. M.: Cloud droplet size distribution broadening during diffusional growth: ripening amplified by deactivation and reactivation, Atmos. Chem. Phys., 18, 7313–7328, 10.5194/acp-18-7313-2018, 2018.