ACPAtmospheric Chemistry and PhysicsACPAtmos. Chem. Phys.1680-7324Copernicus PublicationsGöttingen, Germany10.5194/acp-19-1413-2019Understanding aerosol–cloud interactions through modeling the development
of orographic cumulus congestus during IPHExUnderstanding aerosol–cloud interactionsDuanYajuanhttps://orcid.org/0000-0002-8072-4310PettersMarkus D.https://orcid.org/0000-0002-4082-1693BarrosAna P.barros@duke.eduDepartment of Civil and Environmental Engineering, Duke University, Durham, NC, USADepartment of Marine Earth and Atmospheric Sciences, North Carolina State University, Raleigh, NC, USAAna P. Barros (barros@duke.edu)4February20191931413143726April201814May201816December201821December2018This work is licensed under the Creative Commons Attribution 4.0 International License. To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/This article is available from https://acp.copernicus.org/articles/19/1413/2019/acp-19-1413-2019.htmlThe full text article is available as a PDF file from https://acp.copernicus.org/articles/19/1413/2019/acp-19-1413-2019.pdf
A new cloud parcel model (CPM) including activation,
condensation, collision–coalescence, and lateral entrainment processes is
used to investigate aerosol–cloud interactions (ACIs) in cumulus development
prior to rainfall onset. The CPM was applied with surface aerosol
measurements to predict the vertical structure of cloud development at early
stages, and the model results were evaluated against airborne observations of
cloud microphysics and thermodynamic conditions collected during the
Integrated Precipitation and Hydrology Experiment (IPHEx) in the inner region
of the southern Appalachian Mountains (SAM). Sensitivity analysis was
conducted to examine the model response to variations in key ACI
physiochemical parameters and initial conditions. The CPM sensitivities
mirror those found in parcel models without entrainment and
collision–coalescence, except for the evolution of the droplet spectrum and
liquid water content with height. Simulated cloud droplet number
concentrations (CDNCs) exhibit high sensitivity to variations in the initial
aerosol concentration at cloud base, but weak sensitivity to bulk aerosol
hygroscopicity. The condensation coefficient ac plays a governing
role in determining the evolution of CDNC, liquid water content (LWC), and
cloud droplet spectra (CDS) in time and with height. Lower values of
ac lead to higher CDNCs and broader CDS above cloud base, and
higher maximum supersaturation near cloud base. Analysis of model simulations
reveals that competitive interference among turbulent dispersion, activation,
and droplet growth processes modulates spectral width and explains the
emergence of bimodal CDS and CDNC heterogeneity in aircraft measurements from
different cloud regions and at different heights. Parameterization of
nonlinear interactions among entrainment, condensational growth, and
collision–coalescence processes is therefore necessary to simulate the
vertical structures of CDNCs and CDSs in convective clouds. Comparisons of
model predictions with data suggest that the representation of lateral
entrainment remains challenging due to the spatial heterogeneity of the
convective boundary layer and the intricate 3-D circulations in mountainous
regions.
Introduction
Atmospheric aerosols produced by dramatically increased
industrialization and urbanization exert a large impact on the climate system
and the hydrological cycle (Koren et al., 2008; Ramanathan et al., 2001; Tao
et al., 2012). Aerosols influence the Earth–atmosphere system primarily via
two mechanisms: a radiative (direct) effect and a microphysical (indirect)
effect (Rosenfeld et al., 2008). The direct effect on the Earth's energy
budget occurs via the scattering and absorption of shortwave and longwave
radiation in the atmosphere, hence modulating the net radiation and climate
(Haywood and Boucher, 2000; Ramanathan et al., 2001). The indirect effect is
related to aerosols as cloud condensation nuclei (CCN) or ice nuclei (IN)
alter microphysical properties and consequently affect cloud radiative
properties and precipitation efficiency (Jiang et al., 2008; Lohmann and
Feichter, 2005; McFiggans et al., 2006). In particular, an increase in
aerosol concentration results in an enhanced cloud droplet number
concentration (CDNC), smaller average drop size, and increased cloud albedo
(Twomey, 1977). Smaller cloud droplets are associated with lower collection
and coalescence efficiency, slower drop growth, and reduced precipitation,
thus leading to longer cloud lifetimes (Albrecht, 1989; Andreae and
Rosenfeld, 2008; Khain et al., 2005). Over complex terrain in California and
Israel, Givati and Rosenfeld (2004) attributed a reduction in annual
precipitation of 15 %–25 % to air-pollution aerosols from upwind
urban areas. By comparing two scenarios of maritime and continental aerosols,
Lynn et al. (2007) found that simulations with maritime aerosols with
relatively lower aerosol number concentrations yielded 30 % more
precipitation than continental aerosols over a mountain slope. Such local
effects can translate into large spatial shifts in clouds and precipitation,
as aerosol–cloud interactions (ACIs) inducing suppression of precipitation
upwind could give rise to the enhancement of precipitation downwind
(Muhlbauer and Lohmann, 2008), thus modifying the spatial distribution of
orographic precipitation, transferring precipitation from one watershed to
another, and strongly influencing the local and regional hydrology. Yang et
al. (2016) examined the reasons for warm rain suppression due to increased
air pollution in the Mt. Hua area in central China. They demonstrated that
weakened valley–ridge circulations because of aerosol–radiation
interactions and lower water vapor concentrations in the valley led to the
suppression of convection and precipitation in the mountain. A study of
thermally driven orographic clouds over a tropical island during the Dominica
Experiment (DOMEX) field campaign found that atmospheric moisture was the
predominant constraint in cloud and precipitation formation over the aerosol
effect, and the surface aerosol source has the strongest influence on
precipitation under unfavorable environmental conditions for cloud growth
(Nugent et al., 2016). Barros et al. (2018) showed that model simulations
using aerosol activation spectra from local sources and activation spectra
from remote aerosol sources resulted in a significant spatial and temporal
redistribution of precipitation in the central Himalayas, including changes
in cloud dynamics and the vertical distribution of hydrometeors. The latter
is the basis for remote sensing measurements of precipitation, and therefore
understanding how ACIs modify precipitation structure is key to improving
retrievals in mountainous regions (e.g., Duan et al., 2015).
In the southern Appalachian Mountains (SAM, Fig. 1), persistent low-level
clouds and fog (LLCF) play a governing role in warm-season rainfall by
increasing the frequency and duration of light rainfall and drizzle, and by
enhancing storm rainfall via seeder–feeder interactions (SFIs; Wilson and
Barros, 2014, 2015 and 2017; Duan and Barros, 2017). SFI refers to the
modification of cloud and raindrop size distributions when precipitation
from above (seeder clouds) falls through lower cloud layers (feeder clouds)
to significantly enhance drop collision–coalescence efficiency and rainfall
rates. Albeit with large spatial variability, microphysical observations and
idealized model simulations of the dynamical evolution of raindrop size
distributions (RDSDs) with height show that SFIs in the lower atmosphere can
explain a 1 order of magnitude increase in rainfall rate at low elevations in
the SAM similar to orographic enhancement at higher elevations. Understanding
and modeling the spatial variability of the vertical microstructure of
clouds in complex terrain is therefore key to understanding precipitation
processes toward improving rainfall estimation and prediction. Whereas
previous studies linked LLCF in the SAM to high biogenic aerosol loading
produced locally with occasional influx from remote pollution sources (Link
et al., 2015; Lowenthal et al., 2009), a quantitative understanding of the
indirect effect of aerosols on clouds with implications for precipitation
dynamics including SFIs is lacking. The purpose of this study is to
investigate ACI-integrating models and observations collected during IPHEx
(Integrated Precipitation and Hydrology Experiment; Barros et al., 2014) with
a focus on the evolution of cloud droplet spectra (CDS) with height. This is
an important first step toward understanding spatial variability in the
vertical structure of cloud microphysics that underlies the observed spatial
and temporal heterogeneity of SFIs.
(a) Study region of the IPHEx campaign in the SAM
(highlighted in the black box), as shown in context of a large-scale map of
the southeastern United States. (b) Topographic map of the SAM
including the two ground-based IPHEx observation sites referred to in this
study. FB valley denotes French Broad valley.
The representation of clouds and precipitation in numerical models relies on
parameterizations of multi-scale processes with uncertainty that depends on
the model temporal and spatial resolution (Khairoutdinov et al., 2005;
Randall et al., 2003). For example, the characteristic timescale of
condensational growth of submicron-size droplets is on the order of 1 ms,
and length scales of individual drops range from micrometers to centimeters
(Pinsky and Khain, 2002), which is a scale gap of 5 to 9 orders of magnitude
with respect to the spatial resolution of cloud-resolving models (km).
Detailed 2-D and 3-D models that explicitly resolve cloud formation and
microphysical processes with varying degrees of completeness are available in
the literature (Fan et al., 2009; Leroy et al., 2009; Muhlbauer et
al., 2010). However, the wide range of length (µm–m) and
timescales (ms–s) associated with aerosol–cloud–precipitation interactions
(ACPIs) poses significant challenges for model spatial and temporal
resolution. Analysis of high resolution (∼1 km) numerical weather
prediction (NWP) simulations in the SAM for various hydrometeorological
regimes using different Weather Research and Forecasting (WRF) physical
parameterizations concluded that cloud development and cloud vertical
microphysical structure are inadequate to predict the spatial and temporal
variability of rainfall rate and rainfall microphysics at the ground (Wilson
and Barros, 2015, 2017). In particular, WRF simulations using six different
microphysical parameterization schemes were analyzed to characterize the
spatiotemporal evolution of low-level moisture fields in the SAM under weak
and strong synoptic conditions. The simulations could not capture persistent
LLCF and, in particular, the midday rainfall peak observed in this region
(Duan and Barros, 2017; Wilson and Barros, 2015). Furthermore, simulations
exploring the use of different planetary boundary layer (PBL)
parameterizations in WRF could not replicate the observed vertical structure
of LLCF, thus failing to reproduce the reverse orographic enhancement linked
to SFI and consequently underestimating surface rainfall intensity (Duan and
Barros, 2017; Wilson and Barros, 2014, 2015, 2017).
An alternative modeling approach to investigate ACI at fine resolution is the
cloud parcel model (CPM). Typically, CPMs simulate aerosol activation and
cloud droplet growth, as well as thermodynamic adaptation of ascending air
parcels at micrometer and millisecond scales (Abdul-Razzak et al., 1998;
Cooper et al., 1997; Flossmann et al., 1985; Jacobson and Turco, 1995;
Kerkweg et al., 2003; Nenes et al., 2001; Pinsky and Khain, 2002; Snider et
al., 2003). A synthesis of model formulations including spectral binning
strategy, principal physical processes (i.e., condensational growth,
collision–coalescence, entrainment), and numerical implementation is
presented in Table 1 for CPMs frequently referred to in the peer-reviewed
literature. The CPM used in this study (the Duke CPM, DCPM) explicitly solves
the cloud microphysics of condensation, collision–coalescence, and lateral
entrainment processes (first reported by Duan et al., 2017; Duan, 2017). The
DCPM was formulated and implemented to be seamlessly coupled to an existing
rainfall microphysics column model describing the stochastic dynamics of
raindrop size distributions (bounce, collision–coalescence, and breakup
mechanisms) (Prat and Barros, 2007b; Prat et al., 2012; Testik et al., 2011),
which in turn is coupled to a radar model. The overarching motivation for the
coupled parcel–rainshaft model is to simulate end-to-end ACPIs from the time
of CN (condensation nuclei) activation to the time
raindrops reach the ground. This framework enables investigating the impact
of aerosol heterogeneity on the vertical structure of warm-season
precipitation, and ultimately how this affects radar reflectivity
measurements and quantitative precipitation estimation (QPE). Here, the focus
is strictly on ACI leveraging IPHEx observations to drive, constrain, and
evaluate the model.
Cloud parcel models with detailed microphysics from the literature
and in this study (Duke CPM). NA denotes information is not described in the
reference paper.
Parcel modelBinningCondensationCoalescenceEntrainmentNumericsAbdul-Razzak etDiscreteLeaitch et al. (1986)Not includedNot includedLSODE solveral. (1998)(Hindmarsh, 1983)Cooper et al. (1997)MovingFukuta and Walter (1970)Modified Kovetz andNot includedFifth-order Runge–KuttadiscreteOlund (1969)(adaptive size)Flossmann etDiscretePruppacher and Klett (1978)Berry and Reinhardt (1974)Lateral homogeneousNAal. (1985)bubble modelJacobson andHybridJacobson and Turco (1995)Jacobson et al. (1994)Not includedSMVGEAR (JacobsonTurco (1995)discreteand Turco, 1994)Kerkweg etDiscretePruppacher and Klett (1997)Bott (2000)Lateral homogeneousNAal. (2003)bubble modelNenes et al.MovingPruppacher and Klett (1997),Not includedNot includedLSODE solver(2001, 2002)discreteSeinfeld and Pandis (1998)(Hindmarsh, 1983)Pinsky andMovingPruppacher and Klett (1997)Bott (1998), turbulentNot includedNAKhain (2002)discreteeffect on drop collisionSnider et al. (2003)DiscreteZou and Fukuta (1999)Not includedNot includedNADuke CPMMovingPruppacher and Klett (1997),Bott (1998), turbulentLateral homogeneousFifth-order Runge–KuttadiscreteSeinfeld and Pandis (2006)effect on drop collisionbubble and jet model(adaptive size)
The paper is organized as follows. The mathematical formulation of the
cloud parcel model is described in Sect. 2. Section 3 presents the IPHEx
measurements relevant for the modeling study, followed by model sensitivity
tests and a comparison of model results with in situ observations in Sect. 4.
Finally, the main research findings and outlook of ongoing and future
research are presented in Sect. 5.
Model description
A new cloud parcel model (or Duke CPM – DCPM – for specificity)
was developed to explicitly solve key cloud microphysical processes and
predict the evolution of cloud droplet spectra originating from aerosol
distributions of uniform chemical composition (see the last row of Table 1
for details). The model synthesizes well-established theories and physical
parameterizations in the literature. In particular, condensation and lateral
homogeneous entrainment follow the formulations of Pruppacher and Klett
(1997) and Seinfeld and Pandis (2006), modified to incorporate the single
parameter representation of aerosol hygroscopicity (Petters and Kreidenweis,
2007). The representation of collision–coalescence processes takes into
account the variation of collision efficiencies with height (Pinsky et
al., 2001) and the effects of turbulence on drop collision efficiency as per
Pinsky et al. (2008).
The model discretizes the CDS on a finite number of bins (nbin) using a
discrete geometric volume-size distribution, spanning a large size range with fewer
bins and a very fine discretization in the small droplet sizes to improve
computational efficiency (Kumar and Ramkrishna, 1996; Prat and Barros,
2007a). The characteristic single-particle volumes in adjacent bins are
expressed as vi+1=Vratvi, where Vrat is a
constant volume ratio (Jacobson, 2005). When condensation and coalescence are
solved simultaneously, a traditional stationary (time-invariant) grid
structure often introduces artificial broadening of the droplet spectrum by
reassigning droplets to fixed bins through interpolation that is numerical
diffusion (Cooper et al., 1997; Pinsky and Khain, 2002). To eliminate
numerical diffusion artifacts, the model implementation relies on a moving
grid structure so that an initial size distribution can change with time
according to condensational growth. This approach allows particles in each
bin to grow by condensation to their exact transient sizes without
partitioning between adjacent size bins. Subsequently, collision and
coalescence are resolved on the moving bins that evolve from condensation.
The DCPM predicts number and volume concentrations of cloud droplets and
interstitial aerosols, liquid water content (LWC), effective drop radius,
reflectivity, and other moments of the cloud droplet size distribution. It also tracks
thermodynamic conditions (e.g., supersaturation, temperature, pressure) of
the rising air parcel. The flowchart in Fig. 2 describes the key elements and
linkages in the parcel model, including microphysical processes, and main
inputs and outputs. The performance of the DCPM was first evaluated by
comparing its dependence on different parameters with the results from the
numerical simulations reported by Ghan et al. (2011) in Sect. S1 of the
Supplement. Specifically, Figs. S1–S6 in the Supplement demonstrate that the
simulated maximum supersaturation and number fraction activated from the DCPM
are in good agreement with the numerical solutions in Ghan et al. (2011) for
a wide range of updraft velocities, aerosol number concentrations, geometric
mean radii, geometric standard deviations, hygroscopicity, and condensation
coefficients. Model formulation of key processes is detailed below. A
glossary of symbols as well as auxiliary formulae are given in Appendix A.
Flowchart of the main inputs, microphysical processes, and main
outputs of the DCPM. Equation numbers refer to formulae in Sect. 2.
Condensation growth with entrainment
The time variation of the parcel's temperature (T) can be written as
-dTdt=gVcp+Lcpdwvdt+μ[Lcpwv-w′v+T-T′]V,
where the first two terms on the right-hand side represent
the adiabatic cooling of a rising parcel, and the third term describes the
modulation by entraining ambient dry air with entrainment rate μ. The
vertical profiles of the ambient temperature (T′) and water vapor mixing
ratio (w′v) can be interpolated from input sounding data from
atmospheric model simulations or radiosonde observations.
The change of the water vapor mixing ratio (wv) in the parcel
over time is described by
dwvdt=-dwLdt-μwv-w′v+wLV.
The change of the parcel's velocity (V) is given by
dVdt=g1+γ(T-T′T′-wL)-μ1+γV2,
where γ=0.5 to include the effect of induced mass acceleration
introduced by Turner (1963).
Due to significant uncertainties and complexities of entrainment and
turbulent mixing (Khain et al., 2000), only lateral entrainment that mixes in
ambient air instantaneously and is homogeneous in the parcel is considered in
the DCPM. Based on observations from McCarthy (1974), the entrainment rate
(μ) is represented by an empirical relationship that describes the influx
of air and ambient particles into the parcel as varying inversely with cloud
radius R. To predict the evolution of cloud radius, two conceptual models
of lateral entrainment are available in the DCPM: the bubble model (Scorer
and Ludlam, 1953) and the jet model (Morton, 1957).
For the bubble model, the change of the radius of a thermal bubble
(RB) over time is given as
dlnRBdt=13(μBV-dlnρadt),
where μB=CB/RB and CB=0.6
(McCarthy, 1974).
For the jet model, the time variation of the radius of a jet plume
(RJ) is expressed by
dlnRJdt=12(μJV-dlnρadt-dlnVdt),
where μJ=CJ/RJ and CJ=0.2
(Squires and Turner, 1962).
The condensational growth rate of droplets in the ith bin (i=1,2,…,nbin) is represented as
dridt=GriS-Seq,i,
where droplet growth via condensation is driven by the difference between the
ambient supersaturation (S) and the droplet equilibrium supersaturation
(Seq,i, see Eq. A4 in Appendix A). The growth coefficient
(G) depends on the physicochemical properties of aerosols (see Eq. A1 in
Appendix A). Microscale perturbations in supersaturation due to air flow
around individual hydrometeors, that is ventilation of the drop boundary
layer, are implicitly parameterized by the modified diffusivity parameter
used in the growth factor equation, which depends on particle size (Eq. A2,
Appendix A).
Assuming S≪1, then (1+S)≈1, and the time variation of the
supersaturation in the parcel can be expressed as
dSdt=αV-γ(dwLdt+μVwL)+μV[LMwRT2T-T′-pMaesMwwv-w′v],
where α and γ depend on temperature and pressure (see Eqs. A5
and A6 in Appendix A; see also Korolev and Mazin, 2003).
During the parcel's ascent, entrainment mixes out cloud droplets and
interstitial aerosols inside the parcel and brings in dry air and aerosol
particles from the environment. Entrained aerosols are exposed to
supersaturated conditions in the parcel; some become activated and
continuously grow into cloud droplets. The rate of change in droplet number
in the ith bin (i=1,2,…,nbin) due to entrainment alone
is
dNidtent=-μVNi-N′i,
where N′(z) is the number concentration of ambient aerosol particles
(i.e., outside the cloud) at altitude z.
The rate of change in the liquid water mixing ratio (wL) in the
parcel is calculated as follows:
dwLdt=4πρw3ρa∑i=1nbin(3Niri2dridt+ri3dNidt).
Collision–coalescence growth
To describe droplet growth by collision–coalescence process, the stochastic
collection equation (SCE) that solves for the time rate of change in the
number concentration is written following Hu and Srivastava (1995):
∂N(v)∂t=12∫0vN(v-v′,t)N(v′,t)C(v-v′,v′)dv′-N(vt)∫0∞N(v′,t)C(v,v′)dv′,
where the first integral on the right-hand side of the equation describes the
production of droplets of volume v resulting from coalescence of smaller
drops, and the second integral accounts for the removal of droplets of volume
v due to coalescence with other droplets. The continuous SCE is discretized
and numerically solved by a linear flux method as outlined by Bott (1998).
This method is mass conservative, introduces minimal numerical diffusion, and
is highly computationally efficient (Kerkweg et al., 2003; Pinsky and Khain,
2002). As noted before, the collision–coalescence process is calculated on a
moving grid with bins modified by condensational growth at each time step.
For two colliding drops of volume of v and v′, the coalescence kernel
C(v,v′) in Eq. (10) is computed as the product of the gravitational
collision kernel K(v,v′) and the coalescence efficiency
Ecoal(v,v′),
Cv,v′=K(vv′)Ecoal(vv′),Kv,v′=9π1613v13+v′132Vt-V′tEcollv,v′,
where Vt(V′t) is the terminal velocity of drop volume v(v′),
and Ecoll(v,v′) is the corresponding collision efficiency.
Ecoal is parameterized following Seifert et al. (2005), who
applied the Beard and Ochs III method (1995) for small raindrops
(dS<300µm), the Low and List (1982) method for
large raindrops (dS>600µm), and used an
interpolation formula for intermediate drops (300µm<dS<600µm), where dS is the diameter of
the small droplet. A simpler and faster option suggested by Beard and Ochs
(1984) is also available in the model. The terminal velocity of hydrometeors
is estimated following Beard (1976, 1977) in three ranges of the particle
diameter (0.5–19 µm, 19 µm–1.07 mm, 1.07–7 mm),
though droplets larger than 40 µm do not form in the early stages
of cloud development. Another approximation by Best (1950) is also available
as an option in the model. The table of drop–drop collision efficiencies at
1 µm resolution developed by Pinsky at al. (2001) is used for
Ecoll. This table was created based on simulations of
hydrodynamic droplet interactions over a broad range of droplet radii
(1–300 µm), including collisions among small cloud droplets as
well as between small cloud droplets and small raindrops. Moreover,
Ecoll was derived at three pressure levels of 1000, 750, and
500 mb and can be interpolated at each level of a rising cloud parcel, thus
taking the increase of Ecoll with height into account. Turbulence
can significantly enhance collision rates especially for small droplets
(below 10 µm in radii) as it increases swept volumes and
collision efficiencies, and influences the collision kernels and droplet
clustering (Khain and Pinsky, 1997; Pinsky et al., 1999, 2000). Considering
different turbulent intensities for typical stratiform, cumulus, and
cumulonimbus clouds, detailed tables of collision kernels and efficiencies in
turbulent flow created by Pinsky et al. (2008) for cloud droplets with radii
below 21 µm are also incorporated in the model.
Numerical formulation
The equations in Sect. 2.1 constitute a stiff system of nonlinear,
first-order ordinary differential equations and involve state variables at
very different scales. For the numerical integration of condensation growth,
a fifth-order Runge–Kutta scheme with Cash–Karp parameters (Cash and Karp,
1990) using adaptive time steps (Press et al., 2007) is employed. At each
time step, the error is estimated using the fourth-order and the fifth-order
Runge–Kutta methods. Because dependent variables differ by several orders of
magnitude, a fractional error (ε) is defined to scale the error
estimate by the magnitude of each variable. Specifically, the time-step size
is adaptive to satisfy a fractional tolerance of 10-7 for all variables.
The initial time step to calculate condensational growth is 5×10-4 s. The maximum time step is set as 10-3 s to ensure the
diffusional growth of drops is precisely simulated and nonactivated
particles reach equilibrium with the parcel supersaturation at each time
step. For the collision–coalescence processes in Sect. 2.2, a simple Euler
method is applied to integrate forward in time. The flux method for solving
the discrete SCE was demonstrated to be numerically stable for various grid
structures and integration time steps when the positive definiteness is
maintained (Bott, 1998). Thus, a time increment of 0.2 s is adequate to
ensure that the available mass in each bin is much larger than the change of
mass in the bin during the redistribution of the mass at one time step.
Relying on separate numerical integration methods for calculating
condensation and collision–coalescence allows us to either include or exclude
each process easily to examine its role individually in cloud formation.
Differential droplet sedimentation can be simulated explicitly in the DCPM
using the Eulerian–Lagrangian framework described by Prat and Barros (2007b).
For small cloud droplets (<40µm) characteristic of the early
stages of cloud formation and development considered in this study, terminal
velocities aloft (e.g., Beard, 1977) are significantly smaller (≤0.06 m s-1) than the parcel updraft (≥0.5 m s-1).
Further, the timescales of condensation and drop–drop interactions are very
short compared to the timescales required to reach terminal velocity which
are size dependent (Guzel and Barros, 2001; Barros et al., 2008). Exploratory
tests with CPM model simulations with and without explicitly resolving
sedimentation in the early stages of cloud formation and development showed
no difference in simulated CDNC and CDS. Thus, explicit sedimentation is
bypassed in the model simulations here, which reduces computational times by
more than 3 orders of magnitude. Terminal velocity differences are,
however, important to determine collision–coalescence outcomes (see
Sect. 2.2).
IPHEx data
The intense observing period (IOP) of the IPHEx field campaign took place
during 1 May–15 June 2014. The study region was centered on the SAM
extending to the nearby Piedmont and Coastal Plain regions of North Carolina
(see maps in Fig. 1). IPHEx was one of the ground validation campaigns after
the launch of NASA's Global Precipitation Measurement (GPM) core satellite.
Further details can be found in the IPHEx science plan (Barros et al., 2014).
Surface measurements in the inner region of the SAM were conducted in the
Pigeon River basin (PRB, Fig. 1b) including a dense network of rain gauges
and disdrometers. During the IPHEx IOP, measurements of surface aerosol
concentrations and size distributions ranging from 0.01 to 10 µm
were collected in Maggie Valley (MV), a tributary of the Pigeon River.
Collocated with aerosol instruments at the MV supersite, the ACHIEVE
(Aerosol, Cloud, Humidity, Interactions Exploring and Validating Enterprise)
platform was also deployed, equipped with W-band (94 GHz) and X-band
(10.4 GHz) radars, a ceilometer, and a microwave radiometer. Two aircraft
were dedicated to the IPHEx campaign. The NASA ER-2 carried multifrequency
radars (e.g., a dual-frequency Ka/Ku, W, X band) and radiometers, and
functioned as the GPM core-satellite sampling simulator from high altitude.
The University of North Dakota (UND) Citation aircraft was instrumented to
characterize the microphysics and dynamical properties of clouds, including
LWC and DSDs from cloud to rainfall drop sizes. Therefore, this data set
offers a great opportunity to investigate ACIs tied to warm-season moist
processes in complex terrain. A detailed description of the specific
measurements relevant to this study is provided below and in Sect. S2.
Surface measurements
Aerosol observations were carried out at the MV supersite (marked as the
yellow star in Fig. 1b) in the inner mountain region during the IPHEx IOP.
The elevation of the MV site is 925 m above mean sea
level (a.m.s.l.). The data set
provides a clear characterization of the size distribution and hygroscopicity
of surface aerosols in this inner mountain valley, which was not available
previously. Nominal dry aerosol size distributions at the surface were
measured by a scanning mobility particle sizer system (SMPS) for particles from 0.01 to 0.5 µm in diameter and a
passive cavity aerosol spectrometer (PCASP; manufactured by Droplet
Measurement Technologies, Inc., Boulder, CO, USA) for particle diameters in
the size range of 0.1–10 µm. The SMPS consists of an
electrostatic classifier (TSI Inc., 3081) and a condensation particle counter
(CPC; TSI Inc., 3771). Note that the relative humidity (RH) of the
differential mobility analyzer (DMA) column is well controlled and the
average RH (±1 standard deviation) of the sheath and sample flows are
2.0±0.8 % and 3.2±0.5 %, respectively. In addition, a
co-located ambient CPC (TSI Inc., 3772), which measures aerosol particles
greater than 10 nm without resolving their size distributions, shows very
close agreement with the SMPS measurements with regard to total number
concentrations of aerosol particles (NCN).
A single column CCN counter (manufactured by Droplet Measurement
Technologies, Inc., Boulder, CO, USA) operated in parallel to the SMPS–CPC
to sample size-resolved CCN concentrations (NCCN). The CCN
instrument cycles through six levels of supersaturation (S) in the range of
0.09 %–0.51 %. At a given S level, each CCN measurement cycle took
approximately 8 min, corresponding to one SMPS scan and buffer time to
adjust supersaturation. On average 178 measurement cycles were completed
daily during the IPHEx IOP, except for occasional interruptions due to
instrument maintenance. CN and CCN distributions were inverted as described
previously (Nguyen et al., 2014; Petters and Petters, 2016). Supersaturation
was calibrated using dried ammonium sulfate and a water activity model
(Christensen and Petters, 2012; Petters and Petters, 2016). The midpoint
activation diameter (D50) is derived from the inverted CN and CCN
distributions (Petters et al., 2009). The hygroscopicity parameter (κ)
is obtained from D50 and instrument supersaturation (Petters and
Kreidenweis, 2007). Detailed time series and diurnal cycles of CN and CCN
measurements are illustrated n in Sect. S2 (Figs. S7–S9). The data show
that the average total number concentration (±1 standard deviation) of
dry aerosol particles is 2487±1239 cm-3 for particles with
diameters between 0.01 and 0.5 µm and 1106±427 cm-3
for particles with diameters between 0.1 and 10 µm in diameter.
No significant diurnal variability in number concentration or hygroscopicity
was present. In addition, a co-located Vaisala weather
transmitter (WXT520) recorded local meteorological conditions continuously
(e.g., wind speed, wind direction, relative humidity, temperature, and
pressure) at 1 s intervals. Diurnal cycles of these local meteorological
variables during the IPHEx IOP are displayed in Fig. S10. The average
meteorological conditions at the sampling site are 0.8±0.6 m s-1
in wind speed, 172±115∘ in wind direction, 77±18 % in
relative humidity, and 19±4∘C in ambient temperature
(arithmetic mean ±1 standard deviation).
Aircraft measurements
Airborne observations from the UND Citation aircraft, equipped with
meteorological (e.g., temperature, pressure, humidity) sensors and
microphysical instruments, are used in this study (Poellot, 2015). Vertical
velocity was obtained from a gust probe, and bulk LWC values were retrieved
from two hot-wire probes (a King-type probe and a Nevzorov probe).
Size-resolved concentrations were measured using three optical probes,
covering droplet diameter from 50 µm to 3 cm: a PMS
two-dimensional cloud (2D-C) probe, a SPEC two-dimensional stereo (2D-S)
probe, and a SPEC high-volume precipitation spectrometer 3 (HVPS-3) probe.
The cloud droplet probe (CDP) measures cloud drop concentrations and size
distributions for particles with diameters between 2 and 50 µm in
30 bin sizes. The droplet sizes are determined by measuring the forward
scattering intensity when droplets transit the sample area of the CDP.
Coincidence errors cause CDP measurements to underestimate droplet
concentrations and broaden droplet spectra. This type of error occurs when
two or more droplets pass through the CDP laser beam simultaneously, and is
highly dependent on droplet concentrations (Lance et al., 2010). The
methodology to correct CDP observations is described in Sect. S2.2
(Fig. S11). The corrected CDP cloud droplet spectra are used in this study to
evaluate model simulated CDNC and CDS. The corrections slightly shift the
measurements to smaller drop sizes (not shown here), thus providing
confidence in the performance of the CDP probe during the IPHEx campaign.
IPHEx case study: 12 June 2014
On 12 June 2014, the W-band radar observations at MV (see Fig. S12) indicate
the formation of cumulus congestus clouds before 12:30 local time (LT) and
further growth into cumulonimbus clouds. Near the MV site, a coordinated
aircraft mission of both the UND Citation and NASR ER-2 was conducted from
12:14 to 15:51 LT on 12 June. Cloud droplet concentrations and size
distributions were sampled at multiple heights above cloud base by conducting
successively higher constant-altitude flight transects through clouds. The
CDP sampled at 1 Hz frequency (corresponding to approximately 90 m in
flight distance), and coincidence errors were taken into account by applying
the correction as described in Sect. S2.1. In particular, the investigation
is limited to the lowest horizontal leg (see the flight track in Fig. 3a,
altitude around 2770–2800 m a.m.s.l.) through the cloud to avoid the
influence of substantial mixing at cloud top that is not treated in the DCPM
currently. The flight period of the first horizontal leg (∼2800 m a.m.s.l.) is from 12:17 to 12:28 LT (See Fig. S13a). In rising
updrafts, in-cloud samples (white plus signs in Fig. 6a and green crosses in
Fig. S13) are defined with a minimum LWC of 0.25 g m-3 from the CDP.
The number of precipitation-size drops in CDNC from the 2-DC probe (measuring
hydrometeors with diameter between 105 µm and 2 mm) is
negligible in these cloudy regions (Fig. S14d), thus confirming that the
aircraft sampled cumulus congestus clouds at the development stage.
Significant topographic heterogeneity (terrain transect indicated by the
thick black line in Fig. 3b) can exert a considerable influence on cloud
formation across this region. As shown in Fig. 3c and d, a pronounced
variability in drop number distributions is manifest in the in-cloud samples
clustered by low (0–1 m s-1) and high (1–2 m s-1) updrafts.
Along the first leg, three cloudy regions are identified near the eastern
ridges (ER, highlighted in the blue dashed box in Fig. 3), over the inner
valley region (in-cloud, IC) region, highlighted by
the blue circle, and near the Eastern Cherokee Reservation (ECR, highlighted
in the blue dashed box). Measurements of in-cloud samples for the three
regions are discussed in Sect. S2.2.
(a) Lowest cloud transect of the UND Citation flight track
on 12 June 2014. The in-cloud observations are identified as white plus signs
and the black asterisk marks MV. From left to right in the map, ECR denotes
Eastern Cherokee Reservation, MP denotes Mount Pisgah, and FB denotes French
Board valley. (b) Updraft velocity variations of the targeted
in-cloud region, denoted by IC in panel updrafts are shown in
(a). The in-cloud samples were
collected at 1 Hz (∼90 m in flight distance) resolution. Cloud
droplet concentrations of the in-cloud samples in IC (b) with low
(0–1 m s-1) and high (1–2 m s-1) updrafts are shown
in panels (c) and (d), respectively. The updraft velocity of each
sample is indicated in the legend. Dotted lines represent the droplet spectra
in the reference subregion within the IC region, within the yellow shaded region
in panel (b).
Eleven samples were collected along ∼1 km flight distance in cloud
region IC (circled in Fig. 3a, vertical velocities shown as blue bars in
Fig. 3b). The droplet spectra in stronger updrafts (see Fig. 3d) have higher
number concentrations and a narrower size range compared to the samples in the
weaker updrafts at the edge of the cloud (see Fig. 3c). This is because in
the stronger (faster) updrafts, the timescale of vertical motion is very
short, thus thwarting entrainment and collision–coalescence processes with
condensation alone governing droplet growth. In the slower updrafts, the
longer timescale of vertical motion enhances entrainment leading to
replenishment of CN, and more importantly collision–coalescence processes to
produce larger droplets, thus broadening the distribution. Aerosol size
distributions are not resolved in the CPC measurements from UND Citation, and
thus surface aerosol measurements at MV (marked as the black asterisk in
Fig. 3a) are used as model input at IC.
Modeling experimentsModel initialization and reference simulation
Dry aerosol concentrations measured by the SMPS and PCASP at MV were averaged
over the first 10 min (averaging interval: 12:14–12:24 LT) of the 12 June
flight and then merged into a single size distribution as shown in Fig. 4.
The combined aerosol distribution at the surface is fit by the
superimposition of four lognormal functions using least-squares minimization.
Table 2 summarizes parameters (total number concentration, geometric mean
diameter, and geometric standard deviation) that characterize the four
lognormal distributions. Notice that aerosol number concentrations below
0.03 µm are underestimated by the fitted cumulative distribution
(cyan curve in Fig. 4). Table 3a summarizes the CPM numerical configuration
parameters, and Table 3b provides model physiochemical parameters and initial
conditions. These particles in such small diameters mostly remain
nonactivated under the supersaturated conditions typical of the atmosphere,
thus, underestimation of their concentrations does not affect cloud
development in the model. The aerosol distribution is discretized into up to
1000 bins, initially covering the size range of 0.01–10 µm. The
grid evolves in time with new bins added as larger particles form by
condensational growth. The grid's high resolution is sufficient to simulate
the partitioning of growing droplets and interstitial aerosols in the parcel.
The aerosols are assumed to be internally mixed so that the hygroscopicity
does not vary with particle size. A constant κ value of 0.14 is
prescribed for each aerosol bin, derived from the average κ from MV
measurements during the first 10 min of the 12 June flight.
Mean surface aerosol size distribution fitted by four lognormal
functions. Observations are merged from the SMPS and PCASP, and are averaged
during the first 10 min (12:14–12:24 LT) of the 12 June flight. Fitted
parameters (total number concentration, geometric mean diameter, and
geometric standard deviation) for each mode are summarized in Table 2.
Lognormal fit parameters characterizing the aerosol number
distribution of four modes. Note N is the total number of aerosol particles per
cm3, Dg is the geometric mean diameter (µm), and
σg is the geometric standard deviation for each mode.
Nsurf and NCBH represent total aerosol number
concentrations at the surface and cloud base height (CBH: 1270 m),
respectively.
During the IPHEx IOP, daytime radiosondes were launched every 3 h at
Asheville, NC (red star in Fig. 1b). This location is on the eastern slopes
of the SAM in the French Broad valley outside of the inner mountain region
far away from the targeted in-cloud region. In addition,
the closest sounding (11:00 LT) was launched much earlier than the flight
take-off time on 12 June 2014. To address the lack of sounding observations
needed for CPM input, high-resolution (0.25 km grid size) WRF simulations
were conducted to extract model soundings in the IC region (highlighted in
Fig. 3a). The detailed configuration of the WRF model for these simulations
(see Fig. 5a for nested grid domains) is described in Sect. S3. Upon
inspection of model results 15 min prior to the flight time, the ensemble
mean of six simulated soundings in valley locations within the IC region was
used to specify environmental conditions at 12:15 LT in CPM simulations
(Fig. 5b). The cloud base height (CBH) is the level where simulated RH is
approximately 100 %. As marked by the horizontal black line in Fig. 5b,
CBH =1270 m above ground level (a.g.l.). at 12:15 LT when the parcel
is released from cloud base. The vertical distribution of simulated
horizontal winds along the aircraft flight path is highly heterogeneous and
anisotropic due to the complex 3-D structure of winds in the complex terrain
of the inner mountain region. This includes shallow thermal upslope winds
between the main valley and surrounding ridges, and ridge–valley
circulations with multiple orientations in lateral valleys as illustrated by
the supplementary animations SA1 (near surface), SA2 (at ridge level), SA3
(at CBH), and SA4 (along the first aircraft flight leg). The animations show
southerly mesoscale horizontal transport above ridges, upslope flows along
the topography in the inner region, and a mesoscale honeycomb-like structure
of weak to moderate updrafts and downdrafts with short-lived intensification
linked to overturning processes across the entire region.
(a) WRF model configuration of four one-way nested domains
at a 15, 5, 1.25, 0.25 km grid resolution, respectively. (b) Vertical
profile of temperature (red solid line) and relative humidity (dashed blue
line) from the spatially averaged WRF sounding columns at IC (see its
location in Fig. 3a). The horizontal dashed line depicts CBH =1270 m a.g.l.
At the IC cloud base, aerosol size distributions are estimated by assuming
that total number concentrations at the surface decay exponentially with a
scale height (HS) of 1000 m (representative of the effectiveness
of the vertical venting mechanism), and geometric mean diameters and
corresponding geometric standard deviations remain constant with height. The
reference HS selected for the control simulation is the height
above ground level where the lifting condensation level (LCL) and the
convective boundary layer (CBL) are the same (i.e., HS∼CBL∼LCL) in the SAM inner valley region
under the flight path. The initial dry aerosol distribution at cloud base
input to the model is the sum of four lognormal distributions with fitting
parameters reported in Table 2. Following Kokhanovsky and de Leeuw (2009),
the number concentration of entrained ambient aerosol particles (N′(z),
see Eq. 8) is calculated based on the assumption that the initial aerosol
distribution at the surface N(0) decays exponentially with height (N′(z)=N(0)exp(-z/HS), where z is the height above ground level).
The initial air parcel excess temperature with respect to the environment is
1.0 K, and the initial pressure and RH of the parcel at cloud base adapt to
cloud surroundings. Vertical velocity measurements at cloud base are not
available. The initial updraft velocity (V0) is assumed to be uniformly
distributed and equal to 0.5 m s-1, consistent with vertical
velocities observed by the W-band radar (see Fig. S12b) and simulated by the
model around the same altitude (2.5 km a.m.s.l.). In summary, the air parcel
in the reference simulation is launched with an initial radius (R) of
500 m, an initial updraft of 0.5 m s-1, and initial aerosol spectra
that are in equilibrium with the humid air at cloud base. When the parcel is
rising, the bubble parameterization with the characteristic length scale R=500 m is used to simulate lateral entrainment (see Eq. 4 in Sect. 2.1).
Ambient aerosol particles penetrate through lateral parcel boundaries with
number concentrations that decrease exponentially with height (HS=1000 m). The turbulent kinetic energy dissipation rate is specified as
200 cm2 s-3, typical of cumulus clouds at early stages. The
parcel reaches cloud top when vertical velocity is near zero. Sensitivity to
parcel radius R, scale height HS, and hygroscopicity κ
will be explored in Sect. 4.2.
Parameter sensitivity analysis
In the past, CPM process studies principally targeted the aerosol–CDNC
closure between model simulations and field observations. For example, Conant
et al. (2004) conducted an aerosol–cloud droplet number closure study
against observations from NASA's Cirrus Regional Study of Tropical Anvils and
Cirrus Layers–Florida Area Cirrus Experiment (CRYSTAL-FACE) using the
adiabatic CPM by Nenes et al. (2001, 2002) that solves activation and
condensation processes only (see Table 1 for details). Using a condensation
coefficient (ac) value of 0.06, they reported that predicted CDNC
was on average within 15 % of the observed CDNC in adiabatic cloud
regions. Fountoukis et al. (2007) used the same CPM as Conant et al. (2004)
under extremely polluted conditions during the 2004 International Consortium
for Atmospheric Research on Transport and Transformation (ICARTT) experiment.
They report that the optimal closure of cloud droplet concentrations was
achieved when the condensation coefficient was 0.06. For marine stratocumulus
clouds sampled during the second Aerosol Characterization Experiment (ACE-2),
Snider et al. (2003) applied the University of Wyoming parcel model to
simulate condensation processes in adiabatic ascent (see Table 1) and
experimented with various condensation coefficients in the range of
0.01–0.81. They hypothesized but did not demonstrate that CDNC
overestimation errors (20 % to 30 % for ac=0.1) in
their CPM simulations could be mitigated by varying the condensation
coefficient as a function of dry particle size instead of using one value for
the entire distribution.
The condensation coefficient of water ac is a key ACI physical
parameter in parcel models that has a strong influence on activation and
droplet growth, as it expresses the probability that vapor molecules impinge
on the water droplet when they strike the air–water interface (McFiggans et
al., 2006). Experimental measurements reviewed by Marek and Straub (2001)
exhibit a strong inverse relationship between pressure and ac
values ranging from 1000 to 100 hPa and from 0.007 to 0.1, respectively
(their Fig. 4). Chodes et al. (1974) measured condensation coefficients in
the range of 0.02–0.05, with a mean of 0.033 from measurements of individual
droplets grown in a thermal diffusion chamber for four different
supersaturation levels. Garnier et al. (1987) repeated the Chodes et
al. (1974) experiments and found that the average condensation coefficient is
closer to 0.02 after correcting their supersaturation calculations. Shaw and
Lamb (1999) conducted extensive simultaneous measurements of the condensation
coefficient and thermal accommodation coefficients (aT) for
individual drops in a levitation cell and reported values for ac
and aT in the ranges of 0.04–0.1 and 0.1–1 with most probable
values of 0.06 and 0.7, respectively. Errors in aerosol–cloud droplet number
closure studies using adiabatic CPMs with laboratory-based condensation
coefficients are well above 10 % and often around 20 %–30 %,
mostly due to overestimation (McFiggans et al., 2006).
This section presents sensitivity tests to assess changes in DCPM simulations
to variations in key inputs and assumptions. Test results are compared with
in-cloud observations from the aircraft to assess the role of individual
state variables and processes for the cumulus congestus' case on 12 June
during IPHEx. Selected parameters are perturbed one at a time while other
assumptions and input parameters remain unchanged as specified in Sect. 4.1.
Table 3b presents a summary of the ranges of physiochemical parameters and
initial conditions tested in the sensitivity analysis.
(a) Summary of model numerical configuration parameters
used in simulations presented here. (b) Summary of physiochemical
parameter ranges used in sensitivity simulations (reference value in bold).
Condensation plays a dominant role in the early stages of cloud formation,
and one key factor in this process is the condensation coefficient
(ac) that governs activation and condensational growth. A
laboratory study by Chuang (2003) reported ac values ranging from
4×10-5 to 1, and experimental values from field campaigns and from
chamber studies of individual droplet growth also differ over a wide range
(0.007–0.1) as reviewed in Sect. 1. Here, ac was made to vary in
the range [0.001,1.0] as per Fountoukis and Nenes (2005). For the targeted
IC region, Fig. 6 shows simulated profiles of updraft velocity,
supersaturation, total CDNC, LWC, and their sensitivity to selected
ac values in comparison with the airborne observations (denoted
by black crosses). Measurements from the IC region along the lowest cloud
transect (blue circle in Fig. 3a) are used to evaluate model performance
since no observations are available in the upper unmixed cloudy areas to
assess the entire vertical profiles simulated by the CPM. Only simulations
with reasonable agreement with the observations are discussed here, and thus
results ac from 0.06 to 1.0 are not shown. Particles larger than
1 µm in diameter are considered cloud droplets and are included
in the integration to calculate LWC. Note that ground elevations under the IC
region vary from 928 m to 1184 m a.m.s.l. (see Fig. 3b), and the region is
on a small hill in the middle of the valley and surrounded by much higher
ridges (terrain elevation ∼1500 m a.m.s.l.). Hereafter, aircraft
measurement altitudes are expressed as above ground level (a.g.l.) to facilitate comparison with
model results.
Sensitivity of the updraft velocity (a),
supersaturation (b), total drop concentration (c), and
LWC (d) to the variations in the condensation coefficient
(ac) as compared to the airborne observations (marked by black
crosses). The horizontal dashed line depicts CBH. In panel (b), the
quasi-steady approximation of supersaturation is calculated based on observed
temperature. It should be kept in mind that airborne measurements of
temperature in clouds are subject to large uncertainties, thus rendering the
derivation of supersaturation unreliable.
Large values of ac (>0.01) have negligible influence on the
vertical velocity profiles shown in Fig. 6a, and it is apparent that
ac has a significant impact on the simulated supersaturation
profiles (Fig. 6b). The black crosses indicate the quasi-steady approximation
of supersaturation (Sqs) calculated according to Eq. (A8) (also
Eq. 3 in Pinsky et al., 2013). Note that large uncertainties can be
associated with aircraft temperature measurements used to estimate
Sqs. Low values of ac strongly inhibit the phase
transfer of water vapor molecules onto aerosol particles (aerosol wetting),
slowing the depletion of water vapor in the parcel and thus substantially
increasing maximum supersaturation (Smax). Consequently, smaller
aerosol particles with high concentrations are activated for higher
Smax values, resulting in a direct increase in cloud droplet
numbers with lower values of ac (Fig. 6c). Overall, these results
are in agreement with earlier studies (Nenes et al., 2002; Simmel et
al., 2005) that investigated the dependence of cloud droplet number
concentrations on the condensation coefficient. Moreover, Fig. 6c shows that
the simulation with ac=0.01 (green line) captures the
observed drop concentrations well between 1500 m and 1600 m a.g.l. (highlighted
in yellow shade), whereas a condensation coefficient that is 1 order of
magnitude lower (ac=0.002, blue line) yields better results for
the observations above 1600 m. As summarized in Table 4, the simulated CDNC
for the region between 1500 m and 1600 m a.g.l. on the hillslope (shaded
in Fig. 6b, reference subregion within the IC region) attains an average CDNC of
354 cm-3 for ac=0.01, which is only ∼1.3 %
higher than the observed average between 1500 m and 1600 m
(349.4 cm-3). The corresponding LWC is also in reasonable agreement
with the range of observed values (Fig. 6d). The simulated CDNCs are
underestimated in the cluster between 1600 and 1750 m (397.5 cm-3),
and the average CDNC simulated using a much lower condensation coefficient
(0.002) is ∼8 % lower than the average CDNC from observations.
Inspection of Fig. 6c suggests that within the IC region there are two clusters of air
parcels at different levels above ground. Model simulations are closer to
observations overlaying the lower terrain (Fig. 3b) using a lower
condensation coefficient. A higher condensation coefficient improves
simulations in the region that includes the maximum updrafts near the
hilltop. Good agreement between the model results and airborne observations
for the lower cluster provides confidence in the conclusions from the
sensitivity tests. Thus, the lower cluster over higher terrain (Fig. 3b
and d) is considered the reference region within the IC region for this study.
Evaluation of the predicted CDNC from simulations using various
condensation coefficients against the averaged observation from the CDP.
aThe averaged CDNC in the predictions for the
indicated altitudes. The DCPM uses above ground level (a.g.l.) as the altitude
coordinate. bDifference (%) =100× (Prediction -
Observation)/Observation. Note that observations between 1500 and
1600 m a.g.l. (349.4 cm-3) over the higher terrain (Fig. 3d) and
between 1600 and 1750 m a.g.l. (397.5 cm-3) over the lower terrain
(Fig. 3c) are calculated by averaging the cluster of five consecutive CDNC
measurements. A shown in Fig. 3b, the two altitudes are approximately the
same with respect to mean sea level (m.s.l.).
The sensitivity of predicted spectra at 1500 m (in solid lines, Fig. 7a) to
ac varying from 0.002 to 0.06 is very high. The observed spectrum
(black dotted line) is the average from five individual CDP measurements
(dotted lines in Fig. 3c and d, also highlighted in the yellow shaded area in
Fig. 3b) between 1500 m and 1600 m a.g.l. (see Fig. 6d for their LWC in
shade). Generally, spectra simulated with lower values of ac are
broader with higher numbers of small droplets, while simulations with large
values of ac yield narrower spectra shifted to larger droplet
sizes. The differences in drop size range and spectra shape can be explained
by inspecting the vertical profiles of the parcel supersaturation and
Seq for six illustrative aerosol particle diameters
(Daero) depicted in Fig. S19. Growth by water vapor condensing
on different sizes of cloud droplets is determined by the difference between
S and Seq (Eq. 6 in Sect. 2.1). At low S, small particles
become interstitial aerosols, and their corresponding Seq remains
in equilibrium with the parcel supersaturation (S-Seq=0). At
high S, because of low ac values, activation of small aerosols
contributes to significant spectra broadening, produces larger CDNC, and
shifts the CDS toward smaller diameters due to slower condensational growth.
This is consistent with Warner (1969), who found that low condensation
coefficients (<0.05) were required to capture the observed dispersion of
droplet spectra in natural clouds, especially for small sizes (i.e., left-hand
side of the spectra). Figure 7b displays the simulated CDS at different
levels for ac=0.01 in comparison with the individual droplet
spectra measured by the CDP. The simulated spectra are representative of the
evolution of cloud droplet distributions in one parcel at different cloud
development stages. The observed spectrum at 1559 m a.g.l. (black dotted
line) and its CDNC (357 cm-3) and LWC (0.37 g m-3) are selected
for comparison based on the agreement between measurements and DCPM
simulations. The results are also consistent with the parameterizations of
CDNC and cloud droplet spectra at different heights, given the updraft
velocity and the number of CCN that can be activated at moderate
supersaturation levels as per Kuba and Fujiyoshi (2006). Simulated spectra at
1500 and 1600 m altitude show very good agreement with the observed number
concentration and drop size range. Below 1600 m, a shift of the unimodal
spectra to larger drop sizes suggests that the condensation process currently
dominates the growth of cloud droplets. Larger drops above 1700 m can grow
by coalescence, leading to the formation of a second mode at larger sizes in
the upper portion of the cloud. For the analyses presented hereafter, we
consider ac=0.01 together with other initial conditions
prescribed for the reference simulation (Sect. 4.1, grey line in the
following figures).
(a) Sensitivity of simulated droplet spectra at 1500 m
(solid lines) to the variations in ac. The black dotted line
reflects the average of five droplet spectra observed by the CDP (dotted
lines in Fig. 3c and d) between 1500 m and 1600 m a.g.l.
(b) Simulated evolution of cloud droplet spectra at 1400, 1500,
1600, 1700, and 1800 m altitude assuming ac=0.01. The black
dotted line denotes the observed droplet spectrum at 1559 m that has similar
total CDNC and LWC as the simulation with ac=0.01 at the same
altitude.
Further examination using data from other cloud and precipitation probes
suggests that concentrations of droplets larger than 30 µm in
diameter are negligible during the first horizontal flight leg. Considering
that droplets with diameters larger than 30–32 µm are required
to trigger effective droplet collisions (Pinsky and Khain, 2002), we conclude
that the collision–coalescence process is not important in the sampled IC
region, and it is unlikely that it contributes to the wide bimodal spectra
observed at early stages of cloud growth. It is noteworthy that small drops
are absent in the simulated spectra, in contrast to the observed spectrum
that exhibits a broad drop size range and two distinct modes (see Fig. 7b).
One possible explanation is that the moving bin grid determined by the
condensation process tends to widen the spectral gap between the growing
droplets and nonactivated aerosol particles in the ascending parcel. A
geometric size distribution with 1000 bins is utilized herein to further
refine the discretization for small particle sizes. Another explanation
relates to the uncertainties of the input sounding extracted from the WRF
simulation. Even though ambient aerosols are entrained continuously through
lateral boundaries, most of them remain as interstitial aerosol particles
because the low supersaturation in the parcel is insufficient to enable
activation (see Fig. 6b). The WRF sounding in Fig. 5b exhibits a lapse rate
of -4.1∘C km-1 from 1270 m (CBH) to 2200 m, corresponding
to stable atmospheric conditions unfavorable for cloud development. To
assess the impact of the environmental conditions on cloud growth, an
additional model simulation was performed by altering the lapse rate at lower
levels (see Appendix B1). The results show that uncertainties in the assumed
environmental thermodynamic conditions (e.g., temperature) impose significant
constraints in the vertical development of clouds, thus posing as a
significant challenge in cloud modeling studies.
Entrainment strength
To access the influence of entrainment on cloud drop concentrations and LWC,
different strengths of lateral entrainment are examined by altering the
initial cloud parcel size R at the cloud base. Figure 8 displays the
vertical profiles of total CDNC and LWC. Cloud droplet spectra formed at
three altitudinal levels (1500 m: solid line, 1600 m: dotted line, and
1700 m: dashed line) for simulations using different initial parcel radii
are compared to the CDP observations in the IC region (denoted by black
crosses in Fig. 8a and b and the black dotted line in Fig. 8c). Entrainment
appears to have a dominant influence on the cloud vertical structure as small
rising parcels associated with higher entrainment dissipate faster by
intensive mixing of dry ambient air through lateral cloud boundaries.
Stronger entrainment strength results in a direct decrease in drop
concentrations and LWC, while it has little influence on the droplet size
range. The best agreement on droplet numbers is between the reference
simulation (R=500 m, ac=0.01; grey line in Fig. 13a) and
the reference subregion within the IC region (between 1500 m and 1600 m a.g.l.),
whereas results for R=1500 m better capture the higher cluster of cloudy
samples (above 1600 m a.g.l.). Recall that when R was held constant, the
higher cluster is better reproduced using ac values 1 order of
magnitude smaller than the reference value. Thus, the sensitivity analysis
illuminates a competitive trade-off with weaker entrainment for higher
condensation coefficients (R=1500 m and ac=0.01, the
orange line in Fig. 8a) when other parameters in the reference simulation
remain the same.
Sensitivity of the total drop concentration (a) and
LWC (b) to the variations in the initial parcel radius (R)
considering lateral entrainment as a bubble model and a jet model.
In panels (a) and (b), the airborne observations are marked by
black crosses, and the horizontal dashed line depicts CBH.
(c) Predicted droplet spectra at three altitudinal levels (1500 m:
solid line, 1600 m: dotted line, and 1700 m: dashed line) using two
parameterization schemes for lateral entrainment: the bubble model with R=500 m (base case, grey lines), R=300 m (cyan lines), and R=1000 m
(green lines); and the jet model with R=500 m (red lines). The black dotted
line reflects the average of five droplet spectra observed by the CDP (dotted
lines in Fig. 3c and d) between 1500 m and 1600 m a.g.l.
Given R=500 m, an additional test was conducted using the jet model
parameterization of lateral entrainment (Eq. 5 in Sect. 2.1). A comparison of
results using the two entrainment parameterizations indicates that the bubble
model (grey line) has stronger entrainment strength than the jet model (red
line) given the same initial parcel size (R=500 m). Nevertheless,
continuous increases in simulated LWC in the upper portion of the cloud (see
Fig. 8b) for both parameterizations are unrealistic (Paluch, 1979). This
problem is attributed to uncertainty in the environmental conditions based on
the WRF sounding. As noted in Fig. B1, decreases in LWC are manifest at the
upper portion of the cloud, as indicated in the simulations with modified
sounding inputs. The lack of sufficient mixing with dry ambient air near
cloud top is an inherent deficiency in the simple parameterization of lateral
homogenous entrainment, assuming decreasing entrainment strength with height,
but this assumption does not significantly affect our conclusions for
in-cloud regions below cloud top.
Initial aerosol concentration
The initial aerosol concentration at cloud base can also have significant
effects on cloud development. Because aerosol size distributions were not
sampled by the aircraft during IPHEx, they are estimated by extrapolating
surface aerosol number concentrations according to an exponential decay with
a given scale height (HS). To probe and characterize the
dependence of droplet formation on aerosol concentrations available at cloud
base, sensitivity to HS was explored by varying its values from
800 to 1200 m in the range of LCL at valley locations along the flight
(Sects. S3 and S4). Figure 9 shows the simulated profiles of the total CDNC
and LWC, and cloud droplet spectra formed at three altitudinal levels
(1500 m: solid line, 1600 m: dotted line, and 1700 m: dashed line). It is
not surprising that aerosol concentrations at cloud base have a substantial
influence on the resulting droplet concentrations. Higher aerosol
concentrations, inferred from larger HS, lead to larger drop
numbers with smaller average droplet sizes, which is known as the first
indirect effect of aerosols (Twomey, 1977). Yet, here, LWC appears
insensitive to the initial aerosol concentration as it is constrained by
moisture content available in the parcel. The best agreement in CDNC between
the DCPM simulations and the average droplet spectra observed by the CDP
(black dotted line in Fig. 9c, see reference subregion within the IC region shaded in
Fig. 3b) is achieved for HS=1000 m, thus within the typical
HS range (550–1100 m) of aerosol number concentration
measurements for remote continental types (Jaenicke, 1993).
Sensitivity of the total drop concentration (a),
LWC (b), and droplet spectra (c) at three altitudinal
levels (1500 m: solid line, 1600 m: dotted line, and 1700 m: dashed line)
to the variations in initial aerosol concentrations at cloud base, as
represented by different values of the scale height (HS).
In panels (a) and (b), the airborne observations are marked by
black crosses, and the horizontal dashed line depicts CBH. The black dotted
line in panel (c) reflects the average of five droplet spectra observed by
the CDP (dotted lines in Fig. 6c and d) between 1500 m and 1600 m a.g.l.
Because of the uncertainty in the characterization of environmental
conditions due to the lack of soundings and the complexity of 3-D
circulations in the inner mountain region, additional CPM simulations were
conducted assuming a well-developed and well-mixed CBL and uniform
distribution of dry aerosol concentrations below CBH. This enables
contrasting the results using the well-mixed CBL and the vertical venting
mechanism to pump low-level aerosol to the atmosphere above the mountain
ridges. These modeling results are discussed in Sect. S4. The surface aerosol
concentration at MV (see Fig. 4) is used as model input at cloud base, and
other input parameters remain as specified in Sect. 4.1. Although there is
good agreement in CDNC between simulations with surface aerosols at cloud
base and the airborne observations using a conservative CPM, there are large
discrepancies between the observed and simulated CDS with respect to spectral
width, peak diameter, and peak concentration number above CBH. More
generally, aerosols exhibit large space–time variability, especially
persistent in regions of complex terrain, with heterogeneous mixing by
different ventilation processes in addition to remote transport (see Figs. 3,
5, and 11 in De Wekker and Kossmann, 2015), all of which can contribute to
the diversity of cloud droplet spectra across the cloud transect (see
Fig. S15a–c). CPMs are column models and cannot capture lateral
heterogeneity.
Hygroscopicity
Another key element in the condensation process is the hygroscopic property
that governs the influence of aerosol chemical composition on CCN activity.
To account for its temporal variability observed during IPHEx, a
κ value varying from 0.1 to 0.4 (within the typical range measured at
the surface site, see Figs. S8a and S9c) is applied uniformly for all
particle sizes. Simulated profiles of total CDNC and LWC are weakly dependent
on hygroscopicity, with only a slightly increase in total CDNC with more
hygroscopic aerosols (Fig. 10). Predicted droplet spectra at three
altitudinal levels (1500 m: solid line, 1600 m: dotted line, and 1700 m:
dashed line) also show little sensitivity to variations in κ. Previous
studies (Sect. S2) report that hygroscopic properties of aerosols vary with
particle size and with height, and consequently hygroscopicity derived from
surface measurements may not be representative of aerosols beneath the cloud
(Pringle et al., 2010). These effects are not accounted for.
Sensitivity of the total drop concentration (a),
LWC (b), and droplet spectra (c) at three altitudinal
levels (1500 m: solid line, 1600 m: dotted line, and 1700 m: dashed line)
to variations in the hygroscopicity parameter (κ). In panels (a)
and (b), the airborne observations are marked by black crosses, and
the horizontal dashed line depicts CBH. The black dotted line in panel (c)
reflects the average of five droplet spectra observed by the CDP (dotted
lines in Fig. 3c and d) between 1500 m and 1600 m a.g.l.
Summary of sensitivity analysis
Under realistic assumptions, the total number concentration and size
distributions from the airborne observations are captured by the
reference simulation well. Sensitivity tests by changing ac in the
range of 0.001–1.0 suggest that the predicted CDNC, CDS, LWC, and
thermodynamic conditions are highly dependent on the condensation
coefficient. At early stages of cloud development, the condensation
coefficient plays a key role in the simulated spectra width and shape, with
increases in ac yielding a shift towards larger droplet sizes and
narrower spectral widths. Entrainment has a substantial impact on the cloud
depth, droplet numbers, and LWC, whereas initial aerosol concentrations have
a strong effect on number concentrations and size distributions of cloud
droplets but induce little effects on LWC. Hygroscopicity has negligible
influence on simulated total CDNC and LWC. Additional tests regarding the
sounding inputs and initial updraft velocity are reported in Appendix B.
Due to the limited data set from the campaign, a specific set of initial
conditions are inferred from surface and airborne observations and reasonable
assumptions are made based on the literature and WRF model results. It is
important to keep in mind the uncertainties associated with the determination
of CBH, which is estimated from the WRF model simulations as concurrent
soundings are not available during IPHEx. If the CBH is lifted by 100 m,
simulations using different ac values (0.002–0.06) are in better
agreement with the airborne measurements of LWC. The CDNC in the reference
region (yellow shade, Fig. 6c) is captured better with a higher
ac value (0.015) but narrower spectra results are associated with
increasing ac values, inconsistent with the observed spectra (not
shown here). These caveats highlight the need for comprehensive concerted
observations of end-to-end processes in future field campaigns.
In previous field campaign follow-up studies, condensation coefficients close
to the modal values from Shaw and Lamb (1999) were specified in adiabatic CPM
simulations of activation and condensation processes to improve CDNC
estimates against near-cloud-base aircraft measurements. This includes
ac=0.06 for warm cumulus during
CRYSTAL-FACE (Conant et al., 2004), ac=0.042 for stratocumulus
during the Coastal Stratocumulus Imposed Perturbation Experiment (CSTRIPE,
Meskhidze et al., 2005), and ac=0.06 for cumuliform and
stratiform clouds during ICARTT (Fountoukis et al., 2007). In the present
study, CPM simulations with entrainment and collision–coalescence processes
are performed to predict CDNC from aircraft measurements several hundred
meters above cloud base. Based on sensitivity tests, model simulations using
a relatively low value of ac (0.01) exhibit CDNC and CDS
consistent with the observed cloud spectra in the inner region of the SAM for
early development of cumulus congestus on 12 June. Exploratory simulations
increasing aerosol number concentrations at cloud base (HS=1200 m, Fig. B3b) show a highly nonlinear response to changes in
ac and R, with the best agreement in CDNC being achieved with
higher ac values (0.03 and 0.06) for weak entrainment
environments (R=1500 m). Further, the corresponding spectra simulated
with higher ac values exhibit larger discrepancies in spectral
width and shape against the observations within the IC region (not shown
here) and thus result in predictions of
inferior skill with regard to cloud vertical development. These results
illustrate the importance of nonlinear trade-offs between entrainment and
condensation for realistic cloud environments (e.g., stronger entrainment
with R=500 m and lower ac=0.01 in the reference simulation,
Sect. 4.2.2).
Finally, the lower value of ac, which is in good agreement with
aircraft observations above cloud base in the present study, is consistent
with diffusion-kinetic theory, which accounts for the feedbacks between latent
heat and temperature in the boundary layer of growing droplets (Fukuta and
Myers, 2007). The entrainment–condensation feedbacks revealed by the DCPM
explain ac values around 0.01 in earlier laboratory experiments
of direct contact condensation on aerosols in ventilated cloud chambers with
horizontal or vertical moist flows (Garnier et al., 1987; Hagen et al., 1989)
in contrast with the most probable value (0.06) found in the levitation cell
by Shaw and Lamb (1999).
Summary and discussion
The vertical microphysical structure of
clouds plays a key role in modulating the rainfall intensity via
seeder–feeder interactions in regions of complex terrain (e.g., Barros and
Lettenmaier, 1994). In this study, a new entraining cloud parcel model (DCPM)
with explicit bin microphysics is presented. Evaluation against classical
cloud parcel models for a range of input parameters showed that the
implementation correctly captures the known microphysics encoded in the
supersaturation balance equation. The DCPM is then applied to investigate
dominant factors in the microphysical development of clouds in the complex
terrain of the inner southern Appalachian Mountains using observations from
the Integrated Precipitation and Hydrology Experiment in 2014 (IPHEx) (Barros
et al., 2014). In particular, the model was applied to simulate the
development of midday cumulus congestus on 12 June 2014 when aircraft
measurements are available during IPHEx. Although the aircraft sampled three
distinct cloud regions along the lowest flight transect above cloud base, the
target in-cloud region for this study is near the IPHEx supersite at Maggie
Valley in the inner mountain region. Thus, a detailed modeling study could
be conducted leveraging ground-based aerosol measurements and W-band radar
profiles available at Maggie Valley to inform model initialization. Besides
Maggie Valley observations, initial conditions and model parameters were
specified based on a review of the literature when measurements of key input
parameters were not available or cannot be measured by current sensor
technology. Despite observing large variability in cloud microphysical
properties at sub-kilometer scale (∼90 m is the spatial averaging resolution
of the measurements along the flight track), modeling results are in good
agreement with the cloud droplet number concentration spectra and liquid
water content from measurements in the center of the cloud 300–500 m above
cloud base.
In the framework of the cloud parcel model, sensitivity of the simulated
cloud microphysical characteristics to variations in key parameters was
investigated within the context of in situ measurements. Results from
sensitivity tests show that the condensation coefficient (ac)
exerts a profound influence on the droplet concentration, size distribution,
liquid water content, and thermodynamic conditions inside the parcel.
Decreases in ac lead to increases in cloud droplet number,
broader droplet spectra, and higher maximum supersaturation near cloud base.
The case-study during IPHEx reveals that the observed cloud features in the
inner mountain region of the SAM are better captured by a low value of
ac (0.01) and strong entrainment corresponding to parcel radius
R=500 m using the bubble parameterization (Sect. 2.1). Lateral
entrainment is found to play an important role on the vertical structure of
CDNC, CDS and LWC in the cloud. Further, it was shown that with other input
parameters remaining the same as those for the reference simulation, there is a
trade-off between the CDNC sensitivity to entrainment strength and the
condensation coefficient: strong entrainment (meaning the characteristic
scale R in the bubble parameterization is small) is compensated by lower
ac values and vice versa. This competitive interference explains
higher values of ac in previous aerosol–cloud droplet closure
studies using adiabatic parcel models that neither include entrainment nor
collision–coalescence. Initial aerosol concentrations at cloud base also have
a large impact on droplet numbers but negligible influence on liquid water
content. The sensitivity analysis indicates that the cloud droplet growth is
generally insensitive to hygroscopicity (Sect. 4.2.4), and thus the constant
κ value used in this study does not significantly affect the simulated
profiles of droplet number concentration and liquid water content. Analysis
of the effect of the interdependence of initial aerosol concentration,
condensation coefficient, and entrainment strength on the droplet number
concentration revealed ambiguous behavior that could only be resolved by
assessing the properties of the simulated droplet spectra (shape, range)
against the aircraft measurements at different altitudes throughout the
clouds (i.e., well above cloud base). Overall, these findings provide new
insights into key parameters of aerosol–cloud interactions (ACIs) to inform
physical parameterizations of convective cloud development.
Nevertheless, a review of data and model limitations is warranted. First,
regarding data limitations to constrain and force the CPM, reasonable
assumptions were made based on the literature to complement surface and
airborne observations from IPHEx and WRF model simulations due to the lack
of near-cloud-base measurements and soundings. Second, the lateral
homogeneous entrainment assumption in the model implies that entrained
aerosols are mixed instantly across the parcel. This disregards inhomogeneous
supersaturation and microphysical structure inside the cloud associated with
discrete entrainment events on different spatial scales (Baker et al., 1980;
Khain et al., 2000). Turbulent mixing (Krueger et al., 1997) breaks down
entrained blobs of air into smaller scales to form small bounded regions with
uniform yet distinct properties on account of molecular diffusion, thus
potentially leading to considerable spectrum broadening. In addition,
entrainment with dry air at cloud top is an important element to cloud
vertical development (Telford et al., 1984) currently not treated in the
model. Downdrafts induced by the penetration of dry air at cloud top can sink
and mix with updrafts, effectively diluting number concentrations and
broadening droplet spectra in clouds (Telford and Chai, 1980). Another
limitation is the assumption of constant and uniform hygroscopic properties
for all particle sizes. That is, κ is treated as a bulk hygroscopicity
parameter. In reality, the aerosol distribution is an aggregate of particles
with different physicochemical properties, including different shapes,
solubility, and chemical species (Kreidenweis et al., 2003; Nenes et
al., 2002). Even if specified initial aerosol characteristics were to capture
the variation of κ with size, how to track the evolution of κ
as particles among different bins undergo collision and coalescence remains a
challenge. Further research is needed to elucidate the impact of
heterogeneous chemical composition of aerosols and variations with
particle size.
For unstable cloud layers, complexity of in-cloud vertical velocity fields
with localized areas of much stronger updrafts has been found to support the
formation of wide bimodal spectra in cumulus clouds due to in-cloud
nucleation of new droplets from interstitial aerosols when the parcel
supersaturation higher up in the cloud exceeds the cloud base maximum (Pinsky
and Khain, 2002). As a result, this mechanism can lead to the formation of a
secondary mode of small droplets in individual spectra, different from our
observed spectra with a second mode centered at a larger droplet size (Figs. 3
and 7). In this study, however, supersaturation does not increase above the
cloud base maximum under the conditions of the original and modified model
environments, likely attributed to the ambiguities in the sounding input from
WRF, even if direct aircraft measurements, albeit highly uncertain, suggest
otherwise. Because the collision–coalescence efficiency kernels are dependent
on particle size, nonlinear stochastic behavior can also lead to the
development of a second mode of larger drops especially because
collision-break-up mechanisms are not active in the range of drop diameters
present during the initial stages of cloud formation and development (Prat et
al., 2012).
Overall, a numerical experiment consisting of 30 different simulations
corresponding to 30 different parameter combinations was conducted, and the
results suggest that the ranges of parameters that lead to
physically meaningful results consistent with observations are well defined.
The results underline the importance of the nonlinear relationship between
entrainment processes that determine the local- (microscale) and cloud-scale
thermodynamic environment around individual particles on the one hand and
the aerosol condensation coefficient that measures the effectiveness of
condensation processes in the same thermodynamic environment on the other.
Given the multi-scale thermodynamic structure of clouds, these interactions
suggest that condensation coefficients in the natural environment are
transient and spatially variable. Further research is therefore necessary to
arrive at representative ensemble estimates toward reducing ACI uncertainties
in quantitative assessments of the aerosol indirect effect. Future work will
focus on exploring the sensitivity of the DCPM in a multidimensional
parameter space to quantify multiple parameter interactions (Gebremichael and
Barros, 2006; Yildiz and Barros, 2007) on ACI processes using the factorial
design method (Box et al., 1978).
The IPHEx data are accessible at Global Hydrology Resource
Center (GHRC) Distributed Active Archive Center
(https://ghrc.nsstc.nasa.gov/home/field-campaigns/iphex) (Petersen and
Barros, 2018).
Glossary of symbols
accondensation coefficientaTthermal accommodation coefficientcpspecific heat of dry airDv, D′vdiffusivity of water vapor in air, and modifieddiffusivity of water vapor in airessaturation vapor pressureggravitational constantGgrowth coefficientHSscale heightka, k′athermal conductivity of air, and modifiedthermal conductivity of airLlatent heat of evaporationMa, Mwmolecular weight of dry air, and of waterN, N′number concentration of cloud droplets,and of ambient aerosol particlesppressurer, rcradius of cloud droplet, and of dry aerosolparticleRuniversal gas constantRaspecific gas constant for moist airRvspecific gas constant for water vaporRB, RJradius of air bubble, and of convective jetSsupersaturationSeqdroplet equilibrium supersaturationT (T′)temperature of air parcel (ambient air)Vparcel updraft velocityv, v′droplet volumeswLmixing ratio of liquid water in parcelwv (w′v)mixing ratio of water vapor in parcel(and in the environment)κhygroscopicity parameterμentrainment rateρa, ρwdensity of dry air, and of waterσwdroplet surface tension
Additional formulae
G=[ρwRTesDv′Mw+Lρwka′TLMwRT-1]-1,
where the modified diffusivity (D′v) and thermal conductivity
(k′a) of water vapor in air account for non-continuum effects
(Seinfeld and Pandis, 2006) and are described as follows:
D′v=Dv1+Dvacr2πMwRT,k′a=ka1+kaaTrρacp2πMaRT,
where the thermal accommodation coefficient (aT) is taken as 0.96
(Nenes et al., 2001). Additional sensitivity tests of CDNC to aT,
ranging from 0.1 to 1 (Shaw and Lamb, 1999), were conducted, and the resulting
droplet concentrations indicate little sensitivity to this input parameter
(not shown here).
The hygroscopicity parameter (κ) is adopted to characterize the impact
of aerosol chemical composition on CCN activity according to the
κ-Köhler theory (Petters and Kreidenweis, 2007).
Seq,i for droplets in the ith bin (i=1,2,…,nbin) can be written as
Seq,i=ri3-rc,i3ri3-rc,i31-κiexp(2MwσwRTρwri)-1,
where rc,i and ri are the radius of the dry aerosol
particle and the corresponding growing droplet, respectively. Droplet surface
tension (σw) is a function of the parcel temperature
(Pruppacher and Klett, 1997).
α=gMwLcpRT2-gMaRTγ=pMaesMw+MwL2cpRT2
Liquid water content (g m-3) can be expressed as follows:
LWC=4π3ρw∑i=1binsNiri3.
Quasi-steady approximation of supersaturation Sqs (Pinsky et
al., 2013) can be expressed as follows:
Sqs≈A1V4πDvNr‾,
where r‾ is the average droplet radius, and N is the total
droplet number concentration.
A1=gRaT(LRacpRvT-1)
Sensitivity to environmental conditions
To account for the uncertainties associated with the environmental condition
from WRF and examine its impact on cloud formation, one additional
simulation was conducted with modified temperature profiles at the lowest
2 km above CBH (1270 m), as displayed in Fig. B1. Here, we adjusted the
original lapse rate (-4.1∘C km-1 from the WRF sounding,
Fig. 10b) to -7∘C km-1 (Γ1) for 1270–2200 m.
The lapse rate for 2200–3200 m was changed to -4∘C km-1
to keep the ambient temperature below CBH and above 3200 m unchanged. Deeper
clouds are formed in the modified environment, representing a conditionally
unstable atmosphere. LWC is significantly enhanced by faster droplet growth
under fast cooling conditions.
Vertical profiles of the supersaturation (a) and
LWC (b) for simulations with the original WRF sounding (grey lines)
and modified ambient temperature (blue lines). In panel (b), the airborne
observations are marked by black crosses, and the horizontal dashed line
depicts CBH. (c) Predicted droplet spectra at three altitudinal
levels (1500 m: solid line, 1600 m: dotted line, and 1700 m: dashed line)
to the variations in the environmental conditions. The black dotted line
reflects the average of five droplet spectra observed by the CDP (dotted
lines in Fig. 3c and d) between 1500 m and 1600 m a.g.l.
Sensitivity to initial updraft velocity
Cloud dynamics also play a crucial role in the microphysical evolution of
cumulus clouds. One major parameter in the cloud dynamical field is the
updraft velocity. In accordance with the observed vertical velocities by the
aircraft and the W-band radar (see Fig. S12b), a reasonable variability in
the initial updraft velocity at cloud base is introduced to assess its
effects on the parcel supersaturation and cloud droplet concentrations, as
shown in Fig. B2. By varying the initial updraft in a range of
0.1–1.5 m s-1, simulated results display similar vertical velocities
at the observation levels, which are still higher than the measured range
(not shown here). Slight increases in maximum supersaturation result from
larger initial updraft velocities, thus leading to slight enhancement of
total droplet numbers. The simulated spectra show a slightly shift towards
larger drop sizes due to weaker updrafts, which allow more time for cloud
droplets to grow in a rising parcel.
Sensitivity of the supersaturation (a), total drop
concentration (b), and droplet spectra (c) at three
altitudinal levels (1500 m: solid line, 1600 m: dotted line, and 1700 m:
dashed line) to the variations in the initial updraft velocity (V0) at
cloud base. In panel (b), the airborne observations are marked by black
crosses, and the horizontal dashed line depicts CBH. The black dotted line
in panel (c) reflects the average of five droplet spectra observed by the CDP
(dotted lines in Fig. 3c and d) between 1500 m and 1600 m a.g.l.
Sensitivity of the total cloud drop concentration to the variations
in condensation coefficient and entrainment strength (strong: R=500 m,
solid thick lines; weak: R=1500 m, dash-dotted thin lines) assuming
different initial aerosol concentrations at cloud base (a:
HS=1000 m; b: HS=1200 m). The airborne
observations are marked by black crosses, and the horizontal dashed line
depicts CBH.
The supplement related to this article is available online at: https://doi.org/10.5194/acp-19-1413-2019-supplement.
YD developed the Duke cloud parcel model (DCPM) and conducted
the modeling study under the guidance of APB. MDP was the lead researcher
operating the SMPS and CCN systems during IPHEx and provided level-2 data
sets of SMPS and CCN measurements (Sect. 3.1). APB and YD wrote the
manuscript, and MDP provided comments. APB handled the reviews and replies to
reviewers with input from MDP and YD.
The authors declare that they have no conflict of
interest.
Acknowledgements
The manuscript was revised after work originally submitted to ACP and
published in ACPD as Duan et al. (2017). The work was supported in part by
NASA grant NNX16AL16G and NSF Rapid Response Research (RAPID) Collaborative
IPHEx grant with Ana P. Barros (1442039) and Markus D. Petters (1442056). The
authors thank the UND Citation flight scientists, in particular Michael
Poellot, Andrew Heymsfield, and David J. Delene, for the flight data and
advice with airborne data analysis; Si-Chee Tsay and Adrian Loftus for the
deployment and operation of the ACHIEVE instruments and W-band radar
calibrated data; Anna M. Wilson for the deployment and maintenance of Duke's
H2F (Haze to Fog) mobility facility (including the PCASP and rain gauges),
data collection, and analysis; and Andrew Grieshop for loaning the X-ray
neutralizer for the duration of the study. We also thank Kyle Dawson and John
Hader for operating the SMPS and CCN systems in the field and Kyle Dawson for
help with the processing of SMPS and CCN data sets (Sect. 3.1). We also
acknowledge computing resources from Yellowstone
(ark:/85065/d7wd3xhc) at NCAR (allocated to the first author) used
for the WRF simulations. The authors are especially grateful to Neil
Carpenter from the Maggie Valley Sanitary District for his support of IPHEx
activities.
Edited by: Hailong Wang
Reviewed by: four anonymous referees
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