# Large-eddy simulations of marine boundary-layer clouds associated with cold
air outbreak during the ACTIVATE campaign. Part II: aerosol–meteorology–cloud
interaction

###### Abstract

Aerosol effects on micro-/macro-physical properties of marine stratocumulus
clouds over the Western North Atlantic Ocean (WNAO) are investigated using in-
situ measurements and large-eddy simulations (LES) for two cold air outbreak
(CAO) cases (February 28 and March 1, 2020) during the Aerosol Cloud
meTeorology Interactions oVer the western ATlantic Experiment (ACTIVATE). The
LES is able to reproduce the vertical profiles of liquid water content (LWC),
effective radius $r_{\rm eff}$ and the cloud droplet number concentration
$N_{c}$ from fast cloud droplet probe (FCDP) in-situ measurements for both
cases. Furthermore, we show that aerosols affect cloud properties ($N_{c}$,
$r_{\rm eff}$, and LWC) via the prescribed bulk hygroscopicity of aerosols
($\bar{\kappa}$) and aerosol size distributions characteristics. $N_{c}$,
$r_{\rm eff}$, and liquid water path (LWP) are positively correlated to
$\bar{\kappa}$ and aerosol number concentration ($N_{a}$) while cloud
fractional cover (CFC) is insensitive to $\bar{\kappa}$ and aerosol size
distributions for the two cases. The changes to aerosol size distribution
(number concentration, width, and the geometrical diameter) allow us to
disentangle aerosol effects on cloud properties from the meteorological
effects. We also use the LES results to evaluate cloud properties from two
reanalysis products, ERA5 and MERRA-2. Comparing to LES, the ERA5 reanalysis
is able to capture the time evolution of LWP and total cloud coverage within
the study domain during both CAO cases while MERRA-2 underestimates them.

##  1 Introduction

Aerosols and clouds pose the largest uncertainty in climate projection since
they mediate the radiative forcing of the Earth’s atmosphere (Seinfeld et al.
2016). An increased loading of aerosols in the atmosphere reflects more
incoming solar energy to space and consequentially cools the Earth system. The
increased aerosol number concentration $N_{a}$ in an environment with constant
liquid water content (LWC) leads to cloud droplets with smaller size and
larger number concentration $N_{c}$, which makes the cloud more reflective,
often called the first indirect effect, a.k.a. Twomey effect (Twomey 1977).
The reduced droplet sizes can also result in less precipitation and longer
cloud lifetime. The latter effect is known as the second indirect effect
(Albrecht 1989). Cloud radiative properties are determined by both the cloud
macrophysical properties, such as the liquid water path (LWP) and cloud
fractional coverage (CFC) and by the cloud microphysical properties, such as
$N_{c}$ and the effecive radius $r_{\rm eff}$. Global mean change in radiative
forcing due to anthropogenic aerosols, relative to preindustrial era (before
year 1850), is roughly estimated to be between $-1.6$ to
$-0.6\,\rm{W\,m}^{-2}$ with a $68\%$ confidence interval in year 2005-2015
(Bellouin et al. 2020). However, how the anthropogenic aerosols affect LWC and
CFC remains unclear (Bellouin et al. 2020; McCoy et al. 2020), which is due to
the fact that LWC and CFC are predominantly determined by meteorology states
but also modulated by changes in $N_{c}$ through precipitation (Stevens and
Feingold 2009). This is the so-called aerosol-meteorology-cloud-interaction
(AMCI) problem that encompasses a wide range of spatial-temporal scales from
nm-sized aerosol particles to large-scale atmospheric circulations
($\mathcal{O}(100\,\rm{km})$). Global Earth system models and even cloud
resolving models suffer from coarse resolutions such that vital cloud
macro/micro processes in marine boundary layer cannot be physically
represented.

Here, we focus on the AMCI process in marine boundary-layer stratocumulus,
which is a canonical cloud regime for studying AMCI as this regime is often in
an emergent state of precipitation and is sensitive to AMCI (Feingold et al.
2010; Seifert et al. 2015). In this case, an increased $N_{c}$ may lead to
either an increased LWC due to the suppression of precipitation (Albrecht
1989) or a reduced LWC due to enhanced entrainment of dry air (Ackerman et al.
2004). The overall effects of increasing $N_{c}$ on LWC depends on the
meteorology states in different cloud regimes. The suppression of
precipitation may alter CFC by either increasing the cloud lifetime (Albrecht
1989) or by influencing the transitioning from open to closed Rayleigh-Bénard
cells of stratocumulus (Rosenfeld et al. 2006; Wang and Feingold 2009a), or by
altering mesoscale circulation and lower-level moisture convergence (Wang and
Feingold 2009b). Nevertheless, response of LWP and CFC to $N_{c}$ is still
uncertain in both the observation and the general circulation models (GCMs).
GCMs typically show a positive correlation between LWP and $N_{c}$ and between
CFC and $N_{c}$ due to a direct reduction in the autoconversion of cloud
droplets to raindrops by an increased $N_{c}$, which is parameterized for the
collision-coalescence process (Ghan et al. 2016; Bellouin et al. 2020). Using
large-eddy simulations (LES) with prescribed constant $N_{c}$, Seifert et al.
(2015) showed that the suppression of precipitation due to increased $N_{c}$
reduces CFC in trade-wind cumulus. However, this effect is compensated by the
Twomey effect and the overall effect of aerosols on the albedo of cloud is
small. LES with more complete and resolved physical processes, informed and
constrained by observations, is needed to unravel discrepancies in GCMs
regarding AMCI.

AMCI associated with marine cold-air outbreaks (CAO) is poorly understood and
has been rarely studied due to the more complicated CAO cloud processes and a
lack of measurements. de Roode et al. (2019) performed an LES inter-comparison
of a CAO case to quantify the turbulent transport at length scales between 1
and 10 km and to study the sensitivity of the CAO to $N_{c}$ and ice
microphysics. Using the same microphysics scheme (Seifert and Beheng 2006) and
prescribed constant $N_{c}$, the Dutch Atmospheric LES, the Max-Planck
Institute for Meteorology (MPI) LES, and the PArallelized Large Eddy
Simulation Model for Atmospheric and Oceanic Flows (PALM) obtained very
different CFC, LWP, and surface precipitation in both magnitude and timing.
They also show that a reduction of $N_{c}$ results in a stronger
precipitation, smaller LWP and earlier breakup of clouds, which is consistent
with the findings for subtropical marine stratocumulus in Wang and Feingold
(2009a). As marine CAOs are generally associated with mixed-phase clouds
(Fletcher et al. 2016), the proper characterization and simulation of ice
microphysics are expected to be critical for AMCI. Substantial spread among
LES models in ice water content (IWC) due to different parameterizations of
ice microphysics was observed in de Roode et al. (2019). Tornow et al. (2021)
examined the role of the riming process in marine CAO using LES with a
prescribed single-mode lognormal aerosol-size distributions and two-moment
Morrison cloud microphysics scheme. They showed that increasing a diagnostic
ice nuclei particle concentration intensifies early and light precipitation,
which accelerates the stratocumulus breakup. Their study showed that only a
prognostic aerosol treatment produced plausible cloud regime transitions and
indicated that a prognostic INP concentration is needed to capture ice
multiplication near the cloud breakup that has often been observed. However,
these LES studies did not explore how $N_{c}$ impacted by a realistic setup of
several aerosol modes and their hygroscopicity modulates LWP, CFC, and
radiation fluxes during CAO. Therefore, a prognostic $N_{c}$, based on model
resolved meteorology and measured aerosol size distributions and
hygroscopicity, is important in understanding AMCI.

The Western North Atlantic Ocean (WNAO) region is characterized by a
complicated climate system that features weather processes involving a wide
range of spatial-temporal scales (Sorooshian et al. 2020). The sea surface
temperature (SST) in the WNAO exhibits sharp spatial gradients due to the Gulf
stream, which, together with strong wind, lead to strong surface heat fluxes
within the atmospheric boundary layer (Painemal et al. 2021b). This creates
ideal condition for cold air outbreak (CAO) events as investigated in Seethala
et al. (2021) and Li et al. (2021). Aerosols transported from sources over the
continental U.S., generated over ocean from shipping emissions and sea spray,
and produced by long-range transport of smoke and dust (Corral et al. 2021;
Aldhaif et al. 2020, 2021) contribute to the total aerosol number
concentration in WNAO. The AMCI is poorly understood in this region, which is
partly due to limited in-situ measurements of aerosol and cloud microphyscial
processes (Sorooshian et al. 2019). The Aerosol Cloud meTeorology Interactions
oVer the western ATlantic Experiment (ACTIVATE) campaign aims to unravel AMCI
in WNAO by collecting unprecedented in-situ and remote-sensing statistics of
aerosols and cloud properties. To achieve this, the dual-aircraft approach is
being adopted for about 150 flights ($\sim 600$ joint total flight hours)
during 2020-2022 in the WNAO region ($25^{\circ}-50^{\circ}$N,
$60^{\circ}-85^{\circ}$W). The lower-flying HU-25 Falcon (a minimum altitude
of 150 m) focuses on measuring in-situ trace gases, aerosol, cloud properties,
thermodynamics, and precipitation. The higher-flying King Air (nominal flight
altitude of 9 km) simultaneously acquires remote-sensing retrievals of
aerosols and clouds and deploys dropsondes to measure the meteorological
states (Sorooshian et al. 2019).

We aim to study AMCI in the WNAO region by performing LES, constrained and
evaluated by the ACTIVATE measurements. The measured aerosol size
distributions and hygroscopicity, which provide a more realistic cloud
condensation nuclei (CCN) pool, are fed into a two-moment microphysics scheme
in the LES, compared to a fixed CCN for the prognostic $N_{c}$ used in
previous LES studies. To our knowledge, LES investigation of AMCI associated
with CAO with realistic aerosol perturbations in the WNAO region has never
been done before. Furthermore, the ameliorated understanding of AMCI and
quantified aerosol-cloud relationships from LES can serve as a benchmark to
evaluate and improve parameterizations of aerosol-cloud processes in global
and regional models.

Using the same large-scale forcing strategy as in Endo et al. (2015), Li et
al. (2021) investigated the marine boundary-layer (BL) and clouds during two
CAO events (February 28 and March 1, 2020), which are characterized by strong
temporally and spatially varying meteorological states in the WNAO region. It
focused on the sensitivities of WRF-LES to large-scale forcing and surface
heat fluxes constrained by the ACTIVATE measurements. In this companion study
of Li et al. (2021), we focus on aerosol effects on clouds under the two CAO
conditions. As mentioned above, we use WRF-LES with prognostic $N_{c}$ based
on measured aerosol properties, compare model results with the ACTIVATE cloud
measurements, and evaluate cloud macrophysical properties in reanalysis
products for the two CAO events reported in Li et al. (2021). The reminder of
the paper is organized as follows. In section 2, we describe ACTIVATE
measurements, reanalysis data, and satellite retrievals used in this study.
Section 3 summarizes the WRF-LES numerical experiment setup. Section 4
discusses WRF-LES simulated aerosol effects on CAO clouds in two cases and
compared to ACTIVATE measurements. Section 5 compares the LES BL structure and
clouds with reanalysis and satellite retrievals. We conclude in section 6.

##  2 Observations, reanalysis, and satellite retrievals

###  2.1 Aerosol size distribution

Aerosol particles with diameter $d$ between $3-100\,\rm{nm}$ were measured by
the Scanning Mobility Particle Sizer (SMPS, TSI model 3085 differential
mobility analyzer and TSI model 3776 condensation particle counter) and those
with sizes larger than $100\,\rm{nm}$ were measured by the Laser Aerosol
Spectrometer (LAS, TSI model 3340) equipped on Falcon HU-25. The uncertainty
for both SMPS and LAS measurements is better than $\pm 10\%-20\%$ over the
submircron aerosol size range (Moore et al. 2021). The sampling frequency is
1/60 Hz and 1 Hz for SMPS and LAS, respectively.

The black dots in Figure 1 represent the aerosol size distribution averaged
over Below Cloud-Base (BCB) flight legs, sampled by SMPS and LAS within the
study domain (16:00-17:00 UTC) for the February 28 case. Two BCB flight legs
were performed, marked as BCB1 and BCB2, as shown in Figure 15(a) and Figure
16(a). Only particles larger than 10 nm in diameter are shown, as smaller
nucleation-mode particles are not likely contributing to the population of
cloud condensation nuclei at realistic supersaturations. We fit the measured
aerosol size distributions using a log-normal distribution function,

$\frac{{\rm d}N}{{\rm d}\ln
d}=\frac{N^{*}}{\sqrt{2\pi}\ln\sigma}\exp\left[-\frac{(\ln
d-\ln\mu)^{2}}{2\ln^{2}\sigma}\right],$ (1)

where $N^{*}$ is the total aerosol number concentration. $\mu$ and $\sigma$
are the geometric median diameter and the standard deviation, respectively.
The fitted parameters using three log-normal modes are listed in Table 3. The
fitting is validated by comparing the number concentration integrated over the
fitted lognormal distribution $\bar{N}_{\rm fit}=\int{\rm d}N$ to the measured
integrated number concentration of aerosols $\bar{N}_{\rm a}$ during the BCB
flight leg. The Percent Error (PE) in total particle number for the BCB1 and
BCB2 legs are $(\bar{N}_{\rm fit}-\bar{N}_{\rm a})/\bar{N}_{\rm a}\times
100=-3.7\%$ and $-12.6\%$, respectively. The relatively low value of PE
suggests that the fitting is robust.

Figure 1: Aerosol size distributions (black dots) obtained from SMPS and LAS
measurements for the February 28 case during the BCB legs. The error bars
indicate $\pm\sigma$ deviation from the time-averaged aerosol size
distribution during a BCB flight leg. The red curve represents the final
fitted size distribution. The dashed blue curves represent log-normal fitting
of individual modes. Fitted parameters are listed in Table 3. Only particles
with $d\geq 10$ nm are used for the fitting. The coarse mode at $d\geq
1\mu\rm{m}$ is not used for the fitting because of the very low number
concentrations (at least 2 orders of magnitude lower than the accumulation
mode) and uncertainties (large error bars).

The aerosol size distribution for the March 1 case is shown in Figure 2 and
the corresponding fitted parameters and validation are listed in Table 4. The
same to the February 28 case, two BCB flight legs were performed as shown in
Figure 15(b) and Figure 16(b). Two and three log-normal modes are used for the
fitting for BCB1 and BCB2, respectively. The fitting is robust as indicated by
low values of PEs ($3.1\%$ and $1.3\%$). It is worth noting that $\bar{N}_{a}$
from BCB2 is about 2.6 times larger than that from BCB2, which suggests a
substantial spatiotemporal variation of aerosol particles below cloud-base.
Without interactive aerosol sources and realistic boundary conditions, we do
not expect the LES to capture the spatial variation of size distribution and
hygroscopicity of aerosols. Thus a uniform size distribution and
hygroscopicity is used within the simulation domain. The same aerosol
treatment was used in Endo et al. (2015), who found that cloud macrophysical
properties are insensitive, but cloud microphysical properties are sensitive,
to aerosol hygroscopicity. However, they estimated the aerosol hygroscopicity
according to the Köhler theory using the aerosol size distribution and CCN
concentration. We use the direct measurement during the ACTIVATE campaign to
ensure a more robust estimation of the bulk hygroscopicity of aerosols
$\bar{\kappa}$ as discussed below.

i

Figure 2: Same as Figure 1 but for the March 1 case. Note that LAS measurement
data for the first four bins are missing due to the failure of the laser power
on March 1. Therefore they are not included in the fitting procedure.

###  2.2 Hygroscopicity of aerosol particles

The WRF-LES takes bulk hygroscopicity ($\kappa$) of each size mode, which can
be estimated from $\kappa$ and mass of each chemical component. The bulk
$\kappa$ of a solute aerosol particle with mixed component $i$ is given by the
simple volume mixing rule (Petters and Kreidenweis 2007)

$\kappa=\sum_{i}\epsilon_{i}\kappa_{i},$ (2)

where $\kappa_{i}$ is the hygroscopicity parameter of each individual (dry)
component of aerosol particles and is obtained from Table 1 of Petters and
Kreidenweis (2007) for both the non-organic and organic components. The volume
fraction $\epsilon_{i}$ of a component is given by

$\epsilon_{i}=\frac{\frac{m_{i}}{\rho_{i}}}{\sum_{i}\frac{m_{i}}{\rho_{i}}},$
(3)

where $m_{i}$ is the mass concentration of each component and $\rho_{i}$ is
the material density of each component. The mass $m_{i}$ of major components
was measured by an Aerodyne High Resolution Time-of-Flight Aerosol Mass
Spectrometer (HR-ToF-AMS) (DeCarlo et al. 2008). The uncertainty in measured
mass concentrations is up to $50\%$ due to uncertainties in the applied
instrument collection efficiency, which was assumed to be unity for this
dataset based on preliminary comparison with particle-into-liquid sampler
(PILS) measurements. We take the time-averaged $m_{i}$ for each BCB flight leg
to calculate $\epsilon_{i}$. The relative mass concentration of organic
aerosol, sulfate (${\rm SO}_{4}^{2-}$), nitrate (${\rm NO}_{3}^{-}$), and
ammonium (${\rm NH}_{4}^{+}$) from the AMS measurement are listed in Table 5
and the corresponding mass of ${\rm(NH_{4})_{2}SO_{4}}$ and ${\rm
NH_{4}NO_{3}}$ are listed in Table 6. A mass-weighted $\kappa$ is calculated
from AMS-measured organic, sulfate, and nitrate mass and by assuming both
sulfate and nitrate are fully neutralized as ${\rm(NH_{4})_{2}SO_{4}}$ and
${\rm NH_{4}NO_{3}}$ to assign appropriate $\kappa$ values (Table 6). Ammonium
concentrations measured by the AMS support this assumption. Time-averaged
$\bar{\kappa}$ calculated according to Equation (2) is listed in the last
column of Table 5. We use same $\bar{\kappa}$ for different modes of aerosol
size distributions even though Fridlind et al. (2017) indicates that smaller
modes have smaller kappas.

###  2.3 Droplet/ice size distribution

Cloud droplet/ice size distribution, liquid or ice water content (LWC or IWC),
number concentration of cloud droplet (ice crystals) $N_{c}$ ($N_{\rm ice}$),
and effective radius $r_{\rm eff}$ were measured by Fast Cloud Droplet Probe
(FCDP) equipped on Falcon HU-25. The FCDP measures particles in a size range
of $3-50\,\mu{\rm m}$ with an uncertainty of less than $20\%$ (Baumgardner et
al. 2017; Knop et al. 2021). The cutoff is $3.5\,\mu{\rm m}$. The two-
dimensional stereo (2DS) probe (Lawson et al. 2006) equipped on HU-25 measures
size and concentration of cloud/ice particles in the range of
$11.4-1464.9\,\mu{\rm m}$ in diameter with a spatial resolution of
$11.4\,\mu{\rm m}$/pixel (Voigt et al. 2010; Bansmer et al. 2018). However,
the first size bin of 2DS measurement was excluded due to large uncertainties.
Therefore, 2DS measurement covers a size range of $28.5-1464.9\,\mu{\rm m}$ in
the present study.

###  2.4 ERA5 and MERRA-2 reanalysis

As described in Part I (Li et al. 2021), large-scale forcings (i.e.,mositure
and temperature advective tendencies and wind profiles) and surface heat
fluxes to drive the WRF-LES are obtained from hourly model-level and surface-
level ERA5 reanalysis with a mesh grid-size of 31 km (Hersbach et al. 2020).
The 3-hourly model-level and 1-hourly surface-level MERRA-2 (Gelaro et al.
2017) reanalysis with a horizontal resolution of $0.5^{\circ}\times
0.625^{\circ}$ are used to compare with WRF-LES and ERA5.

###  2.5 GOES-16 satellite retrievals

We use retrievals from the Geostationary Operational Environmental Satellite
(GOES) to evaluate ERA5/MERRA-2 and WRF-LES. GOES-16 Advanced Baseline Imager
(ABI) retrievals (LWP, $N_{c}$, and $r_{\rm eff}$) are produced using the
Clouds and Earth’s Radiant Energy System (CERES) Edition 4 algorithms (Minnis
et al. 2021; Trepte et al. 2019) adapted to geostationary satellites (Minnis
et al. 2008). The GOES-16 products have a pixel size of 2 km and a selected
time resolution of 20 minutes.

##  3 LES numerical experiment setup

The LES setup is the same as in Part I (Li et al. 2021). The lateral size of
the LES domain is $L_{x}=L_{y}=60\,\rm{km}$ with a grid spacing of
$dx=dy=300\,\rm{m}$. There are 153 vertical layers up to $z_{\rm
top}=7\,\rm{km}$. The two-moment Morrison cloud microphysics scheme with
prescribed aerosol size modes (see section 2.2.1) and hygroscopicity (see
section 2.2.2) is employed (Endo et al. 2015). The same time-varying large-
scale forcing (i.e., temperature and water vapor mixing ratio tendencies
$\partial_{t}\bar{\theta}$ and $\partial_{t}\bar{q}_{v}$, wind speed $u\&v$
relaxation, and divergence $\bar{D}$) and surface heat fluxes described in
Part I are adopted. To investigate the aerosol effects, we perform simulations
with prescribed aerosol size distributions derived from the ACTIVATE campaign
measurements as described in section 2.2.1. Details of simulations are listed
in Table 1.

Table 1:  List of simulations. “NC” denotes prescribed cloud droplet number concentration and “NA” denotes prescribed aerosol number concentration. BCB flight legs and $\bar{\kappa}$ are consistent with the values listed in Table 6. The mean $\kappa$ of each aerosol components ($\bar{\kappa}$) is used in the simulations unless otherwise specified. $0228\\_\rm{NA1\\_\bar{\kappa}_{org}}$ and $0228\\_\rm{NA1\\_\kappa_{org}^{max}}$ denote the simulations with $\bar{\kappa}_{\rm org}$ and $\kappa^{\rm max}_{\rm org}$, respectively. Simulations $0228\\_$NC and $0301\\_$NC are from Li et al. (2021).  Simulations |  $N_{a}$ [$\rm{cm}^{-3}$] |  $N_{c}$ [$\rm{cm}^{-3}$] | BCB leg | $\bar{\kappa}$
---|---|---|---|---
0228$\\_$NC | – | 650 | – | –
$0228\\_\rm{NA1\\_\bar{\kappa}_{org}}$ | 5593 | – | BCB1 | 0.313
$0228\\_\rm{NA1\\_\kappa_{org}^{max}}$ | 5593 | – | BCB1 | 0.392
0228$\\_{\rm NA}2$ | 5364 | – | BCB2 | 0.341
0301$\\_$NC | – | 450 | – | –
0301$\\_$NA1 | 1434 | – | BCB1 | 0.451
0301$\\_{\rm NA2}$ | 3100 | – | BCB2 | 0.479

##  4 Aerosol-meteorology-cloud interactions

The ultimate goal of this study is to investigate how aerosols affect cloud
micro-/macro-physical processes under different meteorological conditions of
the two CAO cases. We first compare the cloud microphysical properties between
WRF-LES and FCDP measurements. Then, aerosol effects on LWC, CFC, and
radiation are investigated. Finally, we address how aerosols impact the BL
meteorology.

###  4.1 Comparison of cloud microphysical properties

We start with control simulations with constant cloud droplet number
concentration $N_{c}$ ($0228\\_$NC and $0301\\_$NC in Table 1), which are
compared to simulations adopting prescribed aerosol size distributions derived
from in-situ measurements during different BCB flight legs. The constant
$N_{c}$ is estimated from the FCDP measurements during the in-cloud legs of
February 28 and March 1 cases. Figure 3 shows the comparison between WRF-LES
and FCDP vertical profiles of LWC, $\langle N_{c}\rangle$, and $\langle r_{\rm
eff}\rangle$. For the February 28 case, simulation 0228$\\_$NC and
$0228\\_\rm{NA1\\_\bar{\kappa}_{org}}$ yields almost the same LWC and
different $\langle N_{c}\rangle$ and $\langle r_{\rm eff}\rangle$ between
16:00-17:00 UTC. By examining the corresponding statistics shown in Figure
4(a) at flight legs with sufficient statistics, it is evident that simulation
0228$\\_$NC is able to capture the vertical structure of $\langle
N_{c}\rangle$ and $\langle r_{\rm eff}\rangle$ while
$0228\\_\rm{NA1\\_\bar{\kappa}_{org}}$ underestimates them compared to the
FCDP measurements.

The hygroscopiticy of organic aerosols $\kappa_{\rm org}$ is difficult to
determine due to uncertainties of their sources. We perform two simulations
($0228\\_\rm{NA1\\_\bar{\kappa}_{org}}$ and
$0228\\_\rm{NA1\\_\kappa_{org}^{max}}$) with the same prescribed aerosol size
distributions but different $\bar{\kappa}$ (due to different $\kappa_{\rm
org}$) estimated from the in-situ aircraft measurements of mass of aerosol
components during the ACTIVATE campaign for the February 28 case. As discussed
in section 2.2.2, we derive $\bar{\kappa}$ from either the mean or largest
value of $\kappa_{\rm org}$. $\kappa_{\rm org}=0.1$, a mean value from Table 1
of Petters and Kreidenweis (2007), is used to calculate $\bar{\kappa}$ for
simulation $0228\\_\rm{NA1\\_\bar{\kappa}_{org}}$. In simulation
$0228\\_\rm{NA1\\_\kappa_{org}^{max}}$, the upper value $\kappa_{\rm
org}=0.229$ is adopted. As shown in Figure 3, $\langle N_{c}\rangle$ and
$\langle r_{\rm eff}\rangle$ from simulation
$0228\\_\rm{NA1\\_\kappa_{org}^{max}}$ are almost identical to the ones from
$0228\\_\rm{NA1\\_\bar{\kappa}_{org}}$. This is because $\kappa$ of the
organic component is about six times small than of the non-organic components
even though the mass fraction of the organic component is $54.5\%$.

We then investigate how vertical profiles of $\langle N_{c}\rangle$ and
$\langle r_{\rm eff}\rangle$ depend on different aerosol size distributions
obtained from two BCB flight legs for the February 28 case. Simulation
$0228\\_\rm{NA}2$ is the same as $0228\\_\rm{NA1\\_\bar{\kappa}_{org}}$ but
with aerosol size distributions (Figure 2(b)) and $\bar{\kappa}$ derived from
BCB2 (Table 3 and Table 6). Figure 3(a) shows that $\langle N_{c}\rangle$ and
$\langle r_{\rm eff}\rangle$ from simulation
$0228\\_\rm{NA1\\_\bar{\kappa}_{org}}$ (red dots) are very close to the ones
from $0228\\_\rm{NA}2$ (blue open circles), which is due to the fact that
aerosol size distributions from the two BCB flight legs are similar as shown
in Figure 1. It is worth noting that the aerosol (LAS and SMPS) and FCDP
measurements were not carried out simultaneously or collocated as shown in
Figure 16(a) for neither BCB flight legs. Figure 15(a) shows the Falcon flight
trajectory with the contour level representing the measurement time and stars
and squares marking the start and end of BCB1 and BCB2 for the February 28
case. Most of the sampling of FCDP took place around 16:24 UTC (Figure 16(a)),
which is closer to the BCB2 flight leg (Figure 15(a)). This suggests that the
location of aerosol measurements during BCB2 is closer to the FCDP measurement
than that during BCB1, which explains why $\langle N_{c}\rangle$ and $\langle
r_{\rm eff}\rangle$ from simulation $0228\\_\rm{NA}2$ are slightly closer to
FCDP measurements than those from $0228\\_\rm{NA1\\_\bar{\kappa}_{org}}$.
Therefore, the discrepancy of $\langle N_{c}\rangle$ and $\langle r_{\rm
eff}\rangle$ between “NA” simulations and FCDP measurements likely depend on
the collocation between the aerosol measurements and the FCDP measurements.

\begin{overpic}[width=433.62pt]{FCDP_WRF_comp}\put(-1.0,68.5){(a)}\put(-1.0,34.0){(b)}\end{overpic}
Figure 3: Comparison of vertical profiles of LWC, $\langle N_{c}\rangle$, and
$\langle r_{\rm eff}\rangle$ between the WRF-LES and the FCDP sampling. A
threshold of ${\rm LWC}=0.02\,\rm{g\,m}^{-3}$, $3.5\,\mu{\rm m}\leq d_{\rm
eff}\leq 50\,\mu{\rm m}$, and $N_{c}=20\,\rm{cm}^{-3}$ is applied to both the
WRF-LES and the FCDP sampling (black dots). For the WRF-LES, only grid cells
within clouds (vertically and laterally) are averaged to obtain the vertical
profile. The measurement took place between 16:00 UTC to 17:00 UTC for the
February 28 and 15:00 UTC to 16:00 UTC for the March 1 cases. The
corresponding mean vertical profile of LWC, $\langle N_{c}\rangle$, and
$\langle r_{\rm eff}\rangle$ is obtained by averaging three snapshots of WRF-
LES output as the output frequency is 30 minutes. The green stars mark all the
above cloud base (ACB) and below cloud top (BCT) flight legs.

\begin{overpic}[width=433.62pt]{FCDP_0228_NC}\put(0.0,40.0){(a)}\end{overpic}\begin{overpic}[width=433.62pt]{FCDP_0228_NA}\put(0.0,40.0){(b)}\end{overpic}

Figure 4: Corresponding statistics of Figure 3(a) for the February 28 case
with (a) constant $N_{c}$ (simulation 0228$\\_$NC) and (b) constant $N_{a}$
(simulation $0228\\_\rm{NA1\\_\bar{\kappa}_{org}}$). Only flight legs (all ACB
and BCT marked by green stars) within clouds that have sufficient data are
used. The data are binned at those heights with a residual range of $\pm
50\,{\rm m}$ such that at least one model layer is counted at the height of
each flight legs. Smaller residual ranges does not affect the statistics. The
height of the red box represents the bin width and the one of the black box is
rescaled for readability. In the box-and-whisker plot, the binned data extends
horizontally from the 25th (Q1, l.h.s wall of the box) to the 75th (Q3, r.h.s
wall of the box) percentile with the median represented by the splitting line
inside the box, the mean represented by solid squares inside the box, the
minimum ($Q_{\rm min}$) and maximum ($Q_{\rm max}$) values represented by the
left and right end of whiskers, respectively. Here $Q$ denotes values of a
quantity (i.e., LWC, $\langle N_{c}\rangle$, and $\langle r_{\rm
eff}\rangle$). The statistics of $N_{c}$ are a single point as $N_{c}$ is
constant in (a).

Figure 3(b) shows the comparison for the March 1 case. Vertical profiles from
simulation $0301\\_\rm{NC}$ are close to the ones from $0301\\_\rm{NA}1$. The
statistics of vertical profiles from both simulation $0301\\_\rm{NC}$ and
$0301\\_\rm{NA1}$ agree well with the FCDP measurements as shown in Figure 5.
We also perform a simulation with aerosol size distributions from BCB2 shown
in Figure 2(b), the integrated aerosol number concentration ($\bar{N}_{\rm
a}$) of which is about two times larger than the one from aerosol size
distributions shown in Figure 2(a). As expected, $\langle N_{c}\rangle$ from
simulation $0301\\_\rm{NA}2$ is larger than the one from $0301\\_\rm{NA}1$ as
shown in Figure 3(b). This is because the BCB1 flight leg is co-located right
below the FCDP sampling while the BCB2 flight leg is not collocated well with
the FCDP sampling as shown in Figure 15(b) (the contour line between stars and
the thick magenta line).

\begin{overpic}[width=433.62pt]{FCDP_0301_NC}\put(0.0,40.0){(a)}\end{overpic}\begin{overpic}[width=433.62pt]{FCDP_0301_NA}\put(0.0,40.0){(b)}\end{overpic}

Figure 5: Same as Figure 4 but for the March 1 case: simulation (a)
$0301\\_\rm{NC}$ and (b) $0301\\_\rm{NA1}$.

We also examine the diurnal variation of cloud properties by comparing the LES
with the FCDP measurements during flights from 20:47:07 to 21:10:58 UTC and
from 19:43:30 to 20:13:44 UTC for the February 28 and March 1 cases,
respectively. LWC from the LES and FCDP measurement agree well with each other
(Figure 17(a) and Figure 18) for the February 28 case. $N_{c}$ from the NA
simulations capture the FCDP measurement better than the NC simulation.
Interestingly, $r_{\rm eff}$ from the FCDP measurement is captured well by the
NC simulation between $1.7-2.5\,\rm{km}$ and is closer to NA simulations above
$2.5\,\rm{km}$. For the March 1 case, the LES capture the FCDP measurements
well except that it slightly underestimates $r_{\rm eff}$ (Figure 17(b) and
Figure 19). Overall, the LES is able to capture the diurnal variation of cloud
properties.

###  4.2 Impact of different aerosol treatments on clouds and radiation

The comparison to in-situ cloud observations indicates that the WRF-LES
simulations can reasonably capture the vertical distribution of LWC in both
CAO cases. Within the aerosol measurement uncertainties, the prescribed
aerosol size distributions to WRF-LES show different impacts on $N_{c}$ and
other cloud properties between February 28 and March 1. In both cases, the LWC
shows very small sensitivity to different aerosol size distributions.
Therefore, changes in $r_{\rm eff}$ and $N_{c}$ primarily reflect the impact
of aerosols on droplet nucleation, similar to the first indirect effect.
Figure 6 shows the difference of vertical profiles of $r_{\rm eff}$ and
$N_{c}$ between simulation $0228\\_\rm{NA1\\_\bar{\kappa}_{org}}$ and
$0228\\_{\rm NC}$. Interestingly, both $\Delta r_{\rm eff}$ and $\Delta N_{c}$
exhibit monotonic patterns vertically with a relatively larger sensitivity
near cloud top. Figure 7 shows $\Delta r_{\rm eff}$ and $\Delta N_{c}$ for the
March 1 case. Except for the large inhomogeneity at the cloud top and base,
there is a different cloud droplet (number and size) response to the
prescribed aerosols near cloud base.

Figure 6: Evolution of difference of (a) $r_{\rm eff}$ and (b) $N_{c}$
profiles between simulation $0228\\_\rm{NA1\\_\bar{\kappa}_{org}}$ and
0228$\\_$NC averaged during the dropsonde measurement time 16:00-17:00 UTC for
the February 28 case.  Figure 7: Same as Figure 6 but for the March 1 case
(simulation 0301$\\_$NA1 and 0301$\\_$NC averaged between 15:00 and 16:00
UTC).

Ice particles were observed for the March 1 case but were barely detected for
the February 28 case as shown in Figure 20, where vertical profiles of IWC and
$\langle N_{\rm ice}\rangle$ from WRF-LES and 2DS measurements are shown,
respectively. $r_{\rm eff,ice}$ from 2DS sampling is also shown. Neither IWC
nor $\langle N_{\rm ice}\rangle$ are sensitive to aerosols in this case study.
Figure 21 shows the corresponding statistics of IWC and $\langle N_{\rm
ice}\rangle$. $\langle N_{\rm ice}\rangle$ from the WRF-LES agrees reasonably
well with the one from the 2DS sampling while IWC is off; however, the WRF-LES
captures the higher magnitude of IWC in March 1.

To further quantitatively examine the sensitivity of cloud macro-physical
properties (LWP, CFC, and IWP) and micro-physical properties ($N_{c}$ and
$r_{\rm eff}$) to the prescribed aerosols, we compare results between
simulations with prescribed $N_{c}$ and aerosol size distributions. To
quantify the impact of prescribed aerosols in both the sign and the magnitude,
we use the metric of percentage difference (PD), defined as ${\rm
PD}=(\mathcal{Q}_{\rm NA}-\mathcal{Q}_{\rm NC})/\mathcal{Q}_{\rm NC}\times
100\%$ with $\mathcal{Q}_{\rm NC}$ and $\mathcal{Q}_{\rm NA}$ representing
quantities from the NC (baseline) and NA simulations, respectively.
$\mathcal{Q}$ is averaged between 12:00 and 18:00 UTC. For the February 28
case, we also assess the sensitivity of cloud and radiation to $\kappa_{\rm
org}$. The time evolution of differences in liquid and ice water path, cloud
fraction, $\langle N_{c}\rangle$, $\langle r_{\rm eff}\rangle$, and short-wave
(SW) cloud forcing at the top of atmosphere ($\rm{SW_{TOA}}$) between the
control simulation 0228$\\_$NC and the ones with prescribed aerosol size
distributions ($0228\\_\rm{NA1\\_\bar{\kappa}_{org}}$,
$0228\\_\rm{NA1\\_\kappa_{org}^{max}}$, and 0228$\\_$NA2) (based on different
BCB flight legs) for the February 28 case is shown in Figure 8. We first
examine how much NA simulations differ from the NC simulation. LWP from the NA
simulations only changes slightly compared to the NC simulation (PD=$-2.6\%$,
$0.6\%$, and $-0.5\%$ for simulations $0228\\_\rm{NA1\\_\bar{\kappa}_{org}}$,
$0228\\_\rm{NA1\\_\kappa_{org}^{max}}$, and $022\\_{\rm NA}2$, respectively)
while IWP decreases considerably (PD=$-24.8\%$, $-11.6\%$, and $-12.4\%$). The
CFC also decreases (PD=$-14.7\%$, $-15.1\%$, and $-14.9\%$). $N_{c}$ decreases
substantially (PD=$-60.9\%$, $-55.7\%$, and $-55.0\%$). Correspondingly,
$\langle r_{\rm eff}\rangle$ increases (PD=$27.2\%$, $23.8\%$, and $21.5\%$).
$\Delta\rm{SW_{TOA}}$ changes by $0.19\,\rm{W\,m}^{-2}$,
$-0.94\,\rm{W\,m}^{-2}$, and $-0.93\,\rm{W\,m}^{-2}$ for simulations
$0228\\_\rm{NA1\\_\bar{\kappa}_{org}}$,
$0228\\_\rm{NA1\\_\kappa_{org}^{max}}$, and $022\\_{\rm NA}2$, respectively.

To examine the effect of $\kappa$ on these quantities, we compare simulation
$0228\\_\rm{NA1\\_\bar{\kappa}_{org}}$ and
$0228\\_\rm{NA1\\_\kappa_{org}^{max}}$. We use $\Delta{\rm
PD}=(\mathcal{Q}_{\rm NA_{i}}-\mathcal{Q}_{\rm NA_{j}})/\mathcal{Q}_{\rm NC}$
to quantify differences between NA simulations, where the subscripts $\rm
NA_{i}$ and $\rm NA_{j}$ indicate two different NA simulations. $\Delta{\rm
LWP}$ from simulations $0228\\_\rm{NA1\\_\bar{\kappa}_{org}}$ (red solid
circles) and $0228\\_\rm{NA1\\_\kappa_{org}^{max}}$ (red pluses) starts to
differ around 10:00 UTC while $\Delta{\rm IWP}$ starts to differ around 15:00
UTC (Figure 8). The difference of PD between simulation
$0228\\_\rm{NA1\\_\kappa_{org}^{max}}$ and
$0228\\_\rm{NA1\\_\bar{\kappa}_{org}}$ in LWP is
$\Delta\rm{PD_{LWP}}=(0.63-(-2.58))\%=3.21\%$, and in IWP is
$\Delta\rm{PD_{IWP}}=13.11\%$. However, $\Delta\rm{CFC}$ is almost the same
with $\Delta\rm{PD_{CFC}}=-0.44\%$. $\Delta\langle N_{c}\rangle$ and
$\Delta\langle r_{\rm eff}\rangle$ shows considerable difference between
simulations $0228\\_\rm{NA1\\_\bar{\kappa}_{org}}$ and
$0228\\_\rm{NA1\\_\kappa_{org}^{max}}$ with $\Delta\rm{PD_{N_{c}}}=5.22\%$ and
$\Delta\rm{PD_{r_{eff}}}=-3.41\%$, respectively. $\Delta\rm{SW_{TOA}}$
decreases by $1.13\,\rm{W\,m}^{-2}$.

How cloud properties respond to aerosol size distributions from different BCB
flight legs is examined by comparing simulations
$0228\\_\rm{NA1\\_\bar{\kappa}_{org}}$ (red solid circles) and 0228$\\_$NA2
(blue open circles) in Figure 8, in which aerosol size distributions from BCB2
listed in Table 3 is used. Minor differences are observed for $\Delta{\rm
LWP}$ ($\Delta\rm{PD_{LWP}}=1.06\%$) while considerable differences are
evident for $\Delta{\rm IWP}$ ($\Delta\rm{PD_{IWP}}=12.37\%$), $\langle
N_{c}\rangle$ ($\Delta\rm{PD_{N_{c}}}=5.85\%$) and $\langle r_{\rm
eff}\rangle$ ($\Delta\rm{PD_{r_{eff}}}=-5.74\%$). $\Delta\rm{CFC}$
($\Delta\rm{PD_{CFC}}=-0.16\%$) almost has no difference. However, the
magnitude of the CFC vertical-structure exhibits difference as shown in Figure
22. $\Delta\rm{SW_{TOA}}$ decreases by $1.11\,\rm{W\,m}^{-2}$. We further
quantify the aerosol effect on radiative forcing by examining the response of
cloud optical depth $\tau_{\rm c}$ to cloud-top $N_{c}$ via the following
relation (Ghan et al. 2016),

$\frac{\Delta\ln\overline{\tau_{\rm c}}}{\Delta\ln\overline{\langle
N_{c}\rangle}}=\frac{\Delta\ln\overline{\rm LWP}}{\Delta\ln\overline{\langle
N_{c}\rangle}}-\frac{\Delta\ln\overline{\langle r_{\rm
eff}\rangle}}{\Delta\ln\overline{\langle N_{c}\rangle}}.$ (4)

Perturbations of LWP and cloud-top $r_{\rm eff}$ due to $N_{c}$ (cloud-top)
are $\Delta\ln\overline{\rm LWP}/\Delta\ln\overline{\langle
N_{c}\rangle}=0.150$ and $\Delta\ln\overline{\langle r_{\rm
eff}\rangle}/\Delta\ln\overline{\langle N_{c}\rangle}=-0.269$, respectively,
which leads to $\Delta\ln\overline{\tau_{\rm c}}/\Delta\ln\overline{\langle
N_{c}\rangle}=0.419$ according to Equation (4).

For the March 1 case, LWP only changes slightly with PD=$0.06\%$ and $-0.02\%$
for simulations $0301\\_{\rm NA1}$ and $0301\\_{\rm NA2}$ compared to
simulation $0301\\_{\rm NC}$, respectively. PD of IWP is $-0.06\%$ and
$2.34\%$. The CFC decreases with PD=$-3.40\%$ and $-3.36\%$. The magnitude of
the CFC vertical-structure is quite similar as shown in Figure 23. $\langle
N_{c}\rangle$ increases with PD=$12.80\%$ and $70.06\%$. $\langle r_{\rm
eff}\rangle$ decreases with PD=$-1.77\%$ and $-12.77\%$. $\Delta\rm{SW_{TOA}}$
decreases by $1.24\,\rm{W\,m}^{-2}$ and $0.51\,\rm{W\,m}^{-2}$.

Similar to the February 28 case, $\Delta{\rm LWP}$ ($\Delta{\rm
PD_{LWP}}=-0.51\%$ between simulations $0301\\_{\rm NA2}$ and $0301\\_{\rm
NA1}$) and $\Delta{\rm IWP}$ ($\Delta{\rm PD_{IWP}}=2.38\%$) in March 1 are
slightly affected by different prescribed aerosol size distributions while CFC
($\Delta{\rm PD_{CFC}}=-0.15\%$) is insensitive to them. Aerosol size
distributions are quite different (Figure 2) between the two BCB legs (total
$N_{a}$ from the flight leg BCB2 is about 2.16 times larger than that of BCB1)
for the March 1 case, which leads to substantial differences in $\langle
N_{c}\rangle$ ($\Delta{\rm PD_{N_{c}}}=57.26\%$) and $\langle r_{\rm
eff}\rangle$ ($\Delta{\rm PD_{r_{eff}}}=-11.00\%$) as shown in Figure 9.
However, the difference between simulation $0301\\_{\rm NA2}$ and $0301\\_{\rm
NA1}$ in $\Delta\rm{SW_{TOA}}$ is only $0.72\,\rm{W\,m}^{-2}$. Differences in
aerosol size distribution induced susceptibility of LWP and cloud-top $r_{\rm
eff}$ to $N_{c}$ (cloud-top) are $\Delta\ln\overline{\rm
LWP}/\Delta\ln\overline{\langle N_{c}\rangle}=-0.002$ and
$\Delta\ln\overline{\langle r_{\rm eff}\rangle}/\Delta\ln\overline{\langle
N_{c}\rangle}=-0.318$, respectively, which results in a positive perturbation
of $\Delta\ln\overline{\tau_{\rm c}}/\Delta\ln\overline{N_{c}}$ (Equation (4))
of 0.316. The susceptibility of LWP and cloud-top $r_{\rm eff}$ to $N_{c}$
(cloud-top) for both cases are summarized in Table 2. The February 28 case
yields $\Delta\ln\overline{\rm LWP}/\Delta\ln\overline{\langle
N_{c}\rangle}=0.15$, which is close to 0.11 reported in Lee et al. (2009) and
summarized in Table S1 of Glassmeier et al. (2021). Our values are very
different from other LES studies reported in Table S1 of Glassmeier et al.
(2021), which summarized $\Delta\ln\overline{\rm
LWP}/\Delta\ln\overline{\langle N_{c}\rangle}$ due to precipitation or
entrainment. However, we note that both the February 28 and March 1 cases
represent non-precipitating stratocumulous clouds. It is also unclear whether
$\Delta\ln\overline{\rm LWP}/\Delta\ln\overline{\langle N_{c}\rangle}$ is due
to entrainment in these two cases. Overall, these two case-studies suggest
that spatial-temporal variation of aerosol distributions have a profound
effect on $\langle N_{c}\rangle$ and $\langle r_{\rm eff}\rangle$. The effects
on $\Delta{\rm LWP}$, $\Delta{\rm IWP}$, and $\Delta\rm{CFC}$ are less
obvious.

Figure 8: Time-series differences of LWP, CFC, IWP, $\langle N_{c}\rangle$, $\langle r_{\rm eff}\rangle$, and $\rm{SW_{TOA}}$ between the control simulation (0228$\\_$NC) and the ones ($0228\\_\rm{NA1\\_\bar{\kappa}_{org}}$, solid red circles; $0228\\_\rm{NA1\\_\kappa_{org}^{max}}$, red pluses; 0228$\\_$NA2, open blue circles) with prescribed aerosol size distributions for the February 28 case. $\langle N_{c}\rangle$ and $\langle r_{\rm eff}\rangle$ are averaged within clouds ($q_{c}\geq q_{c}^{*}$). The threshold $q_{c}^{\star}=0.02\rm{g\,kg^{-1}}$ is adopted to define the cloud fractional coverage (CFC). CFC is calculated by counting the vertical columns where $q_{c}\geq q_{c}^{\star}$, which is then normalized by the number of total vertical column of the entire domain. LWP includes liquid water and rain. IWP includes ice, graupel, and snow.  Figure 9: Same as Figure 8 but for the March 1 case.  Table 2: Aerosol size distribution induced susceptibility of LWP and cloud-top $r_{\rm eff}$ to $N_{c}$ (cloud-top) for the February 28 (0228$\\_{\rm NA}2$\- $0228\\_\rm{NA1\\_\bar{\kappa}_{org}}$) and March 1 (0301$\\_{\rm NA2}$\- 0301$\\_$NA1) cases, respectively.  Case | $\Delta\ln\overline{\rm LWP}/\Delta\ln\overline{\langle N_{c}\rangle}$ | $-\Delta\ln\overline{\langle r_{\rm eff}\rangle}/\Delta\ln\overline{\langle N_{c}\rangle}$ | $\Delta\ln\overline{\tau_{\rm c}}/\Delta\ln\overline{\langle N_{c}\rangle}$
---|---|---|---
February 28 | 0.150 | 0.269 | 0.419
March 1 | -0.002 | 0.318 | 0.316

###  4.3 Impact of ACI on the boundary layer meteorology

The February 28 case is characterized by a warmer, drier and deeper boundary
layer than the March 1 case (Li et al. 2021) as shown in Figure 24. It also
shows that LES is able to capture the diurnal variation of the meteorological
state (by comparing the LES to dropsonde measurements during the morning and
afternoon flights as shown in Figure 24) and cloud properties for both cases.
In this section, we examine how aerosols impact BL meteorology for these two
contrasting CAO cases.

Differences of vertical profiles averaged within the corresponding dropsonde
circle between NA and NC simulations are shown in Figure 10, where $z$ is the
altitude normalized by the cloud top height. We take simulations
$0228\\_\rm{NA1\\_\bar{\kappa}_{org}}$ and 0301$\\_$NA1 as an example. For
both cases, simulations with prescribed aerosol size distributions yields
larger $\theta$ (red and black curves in Figure 10(a)) and smaller $q_{v}$
(Figure 10(b)) near the inversion top due to the enhanced $d\theta/dt$ (Figure
10(e)) and weakened $dq_{v}/dt$ (Figure 10(f)) by condensation/evaporation,
but there are quite different responses near cloud base between the two cases.
This demonstrates that aerosol affects meteorological states via the case-
dependent response in cloud condensation/evaporation process to aerosol
perturbations. Even for the same case (0228 or 0301), different aerosol
perturbations (0228$\\_$NA2 or 0301$\\_$NA2) have a different impact on the
cloud and thermodynamical processes, in terms of magnitude or vertical
location, as shown in the vertical profiles (gray and orange curves in Figure
10) compared to those of 0228$\\_$NA1 and 0301$\\_$NA1, correspondingly. The
response evolves with time as well. The time evolution of vertical-profiles
difference for the February 28 case is shown in Figure 25 . The aerosol effect
on $\theta$ at the inversion layer evolves from positive to negative and stays
positive within the boundary layer. The opposite behavior of aerosol effect on
$q_{v}$ and $q_{c}$ is observed. Figure 26 shows the one for the March 1 case.
Unlike the February 28 case, the positive effect on $\theta$ and negative
effect on $q_{v}$ and $q_{c}$ of aerosols persist to the end of the simulation
and is more profound near the evolving cloud top as discussed. $\Delta
d\theta/dt$ and $\Delta dq_{v}/dt$ due to condensation shows the most distinct
structure at the cloud top and the cloud base. The response of TKE vertical-
profiles to aerosols are more complicated. It exhibits strong spatial
variations for both February 28 and March 1 cases. Overall, ACI has
discernible but variable effects on the BL meteorology that depend on the BL
structure and clouds.

Figure 10: Difference of vertical profiles between simulation
$0228\\_\rm{NA1\\_\bar{\kappa}_{org}}$ and 0228$\\_$NC (black curves) and
between 0301$\\_$NA1 and 0301$\\_$NC (red curves) averaged during the
dropsonde measurement time (16:00-17:00 UTC for the February 28 case and
15:00-16:00 UTC for the March 1 case). The error bars indicate $\pm\sigma$
deviation from the time-averaged vertical profiles. The gray and orange curves
represent other simulations. $z$ is the normalized height by the height of the
cloud top. $\Delta d\theta/dt$ and $\Delta dq_{v}/dt$ are due to
condensation/evaporation. Data is only visualized until the cloud top. The
vertical profiles are shown in Figure 24.

##  5 Evaluating cloud micro/macro-properties in ERA5 and MERRA-2

In this section, we evaluate ERA5 and MERRA-2 reanalysis by comparing the LWP,
CFC, $N_{c}$, and $r_{\rm eff}$ from LES and GOES-16 to those from ERA5 and
MERRA-2 reanalysis. Both ERA5 and MERRA-2 provide LWP as part of their hourly
single-level data. The CFC field of ERA5/MERRA-2 is defined as the maximum
cloud fraction in the vertical (up to 7 km) based on the model-level LWC data
with a threshold of ${\rm LWC}=0.02\,\rm{g\,cm}^{-3}$ for cloud. Note that
ERA5 and MERRA-2 provide 1-hourly and 3-hourly data (instantaneous field) for
the CFC calculation, respectively. The GOES-16 LWP is corrected using the mean
bias reported in Painemal et al. (2012) and Painemal et al. (2021a).

Figure 11 shows the comparison between LES, GOES-16, ERA5, and MERRA-2 for the
February 28 case. LWP (Figure 11(a)) and CFC (Figure 11(b)) retrieved from
GOES-16 agrees reasonably well with the LES, which boosts our confidence to
evaluate the ERA5 and MERRA-2 using LES. Compared to simulation
$0228\\_\rm{NA1\\_\bar{\kappa}_{org}}$, ERA5 slightly overestimates the LWP
while MERRA-2 underestimates it. Nevertheless, both ERA5 and MERRA-2 capture
the time evolution of LWP well. MERRA-2 has a significantly lower CFC compared
to the LES, while CFC has an opposite time evolution between ERA5 and LES. We
further compare the evolution of vertical structure of LWC and CFC between
ERA5, MERRA-2, and LES. As shown in Figure 12, MERRA-2 underestimates the
magnitude of CFC and LWC compared to the LES. Neither MERRA-2 nor ERA5
captures the vertical structure of CFC and LWC of LES that has an apparent
peak near cloud top.

We also compare $N_{c}$ and $r_{\rm eff}$ retrievals from GOES-16 with the LES
near the top of clouds. GOES-16 $N_{c}$ is derived from cloud effective radius
in $\mu$m and cloud optical depth $\tau$ under the adiabatic assumption. The
adiabatic lapse rate of condensation $\Gamma$ ($\rm{g\,m}^{-4}$) is estimated
from the cloud top temperature and pressure retrievals from GOES-16 (see
section E for details of the estimation). Since several studies have shown the
presence of a systematic positive bias in satellite-based $r_{\rm eff}$
(Painemal et al. 2012; Noble and Hudson 2015; Zhang et al. 2017; Painemal et
al. 2021a), here we use values reported in Painemal et al. (2012) and Painemal
et al. (2021a) for GOES-13 and GOES-16 to correct $r_{\rm eff}$ and, in turn,
correct $N_{c}$ via Equation (5). To be consistent with the sensitivity of
satellite $r_{\rm eff}$ to the cloud uppermost layer, $N_{c}$ and $r_{\rm
eff}$ from WRF-LES are averaged over the cloud top (4 layers, about 150 m).
Figure 11(c) and Figure 11(d) show that $N_{c}$ and $r_{\rm eff}$ from WRF-LES
agree reasonably well with those from GOES-16.

Figure 11: Comparison between the WRF-LES (blue, averaged over all the four
simulations), ERA5 (black), MERRA-2 (red), and GOES-16 (green) for the
February 28 case. The gray dashed-dotted lines represent individual
simulations. LWP is retrieved from hourly single-level (quantities obtained
from the model level) ERA5 and MERRA-2 (starting from 00:30 UTC). The mean LWP
is calculated by averaging over the dropsonde-measurement area. Both ERA5
(hourly) and MERRA-2 (3-hourly) provides Cloud Fractional Coverage (CFC) field
at individual model level. The time evolution of CFC is obtained by extracting
the maximum values of the CFC vertical-profiles below 7 km. Vertical profiles
are obtained by sampling each layer conditionally with a threshold of ${\rm
LWC}=0.02\,\rm{g\,cm}^{-3}$ for clouds. $N_{c}$ and $r_{\rm eff}$ are averaged
over the cloud top (4 layers) from the WRF-LES ouput. ERA5, MERRA-2, and
GOES-16 data are averaged over the dropsonde area. LWP, $N_{c}$, and $r_{\rm
eff}$ from GOES-16 are filtered by cloud optical depth $\geq 3$. GOES-16 CFC
are obtained by normalizing the number of pixels with LWP or IWP $\geq 0$ by
the total number of pixels within the dropsonde measurement area. To reduce
the well-known systematic biases in GOES-16 retrievals, the GOES-16 LWP is
corrected by the mean of the lower $+10\,{\rm g\,m^{-2}}$ and upper $+19\,{\rm
g\,m^{-2}}$ bias bounds reported in Painemal et al. (2012) and Painemal et al.
(2021a). The GOES-16 $r_{\rm eff}$ ($N_{c}$ according to Equation (5)) are
corrected by the mean of lower $-2.4\,\mu{\rm m}$ and upper $-4.0\,\mu{\rm m}$
bias bounds according to Painemal et al. (2012) and Painemal et al. (2021a).
GOES-16 data before 14:00 UTC are excluded because the retrievals are less
reliable for low solar angles.  Figure 12: Evolution of vertical profile of
cloud coverage and LWC up to 7 km for the February 28 case. They are obtained
by sampling each layer conditionally with a threshold of ${\rm
LWC}=0.02\,\rm{g\,cm}^{-3}$. ERA5 and MERRA-2 data are averaged over the
dropsonde area. WRF-LES shows the averaged CFC from four simulations as in
Figure 11.

Figure 13 shows the comparison between LES, GOES-16, and reanalysis for the
March 1 case. The agreement in both magnitude and variation of LWP and CFC
between the LES and GOES-16 is reasonably good. Compared to the LES and
GOES-16, both MERRA-2 and ERA5 underestimate LWP. However ERA5 agrees better
with the LES in the diurnal variation. ERA5 agrees with LES in CFC while
MERRA-2 underestimates CFC. The vertical profiles of LWC and CFC are shown in
Figure 14. Similar to the February 28 case, neither ERA5 nor MERRA-2 capture
the vertical structure of CFC compared to LES. Nevertheless, they exhibit
comparable vertical structure of LWC to the LES. ERA5 has larger CFC (nearly
overcast condition) near cloud base and a LWC maximum in the middle of cloud
layers. MERRA-2 has the lowest LWC and CFC at all heights. GOES-16 gives a
similar $N_{c}$ and $r_{\rm eff}$ compared to LES at the cloud top.

Figure 13: Same as Figure 11 but for the March 1 case. Blue dash-dotted lines
represent the mean of three simulations.  Figure 14: Same as Figure 12 for the
March 1 case. WRF-LES shows the averaged CFC from three simulations as in
Figure 13.

##  6 Discussions and conclusion

Using the WRF-LES, we have simulated two cold-air outbreak (CAO) cases (28
February and 1 March, 2020) observed during the ACTIVATE campaign in the
Western North Atlantic Ocean. The aerosol-meteorology-cloud interaction (AMCI)
during the two CAO events are examined by comparing WRF-LES, measurements,
satellite retrievals, and reanalysis.

Aerosol size distributions measured from airborne aerosol-sampling are
prescribed to the LES experiments, which are compared to previous experiments
with prescribed cloud droplet number concentrations (Li et al. 2021). Cloud
properties from the LES experiments are then validated against the FCDP in-
situ measurements. Log-normal aerosol size distributions are fitted from data
acquired during two below-cloud-base (BCB) flight legs for each case. Bulk
aerosol hygroscopicity estimated from mass of individual aerosol components
measured by the Aerodyne Mass Spectrometer is used in the LES. For organic
species, we need to make assumptions in the component hygroscopicity. To
examine the effect of aerosols, we compared LES results with prescribed
aerosol size distributions from different flight legs and/or with different
assumptions in the estimation of bulk hygroscopicity (denoted as NA-LES) to
the ones with constant cloud droplet number concentration $N_{c}$ (denoted as
NC-LES) obtained from the FCDP sampling. For the February 28 case, vertical
profiles of LWC from the two NA-LES are in good agreement. However, $N_{c}$
($r_{\rm eff}$) from the NC-LES is larger (smaller) than that from NA-LES.
This is speculated to be because the aerosol sampling during the two BCB legs
were not co-located very well with the FCDP sampling in space. For the March 1
case, LWC, $N_{c}$, and $r_{\rm eff}$ from NC-LES agree better with those from
NA-LES using aerosol size distributions derived from the BCB flight leg that
co-located well in space with the FCDP cloud droplet sampling. Our LES-
measurement comparison also demonstrates a strong spatial and temporal
variation of aerosol particle distributions during the CAO events, which adds
challenges to the LES modeling and validation. By comparing LES to the
measurements during flights on the same day but at a later time, we show that
the LES captures the diurnal variation of cloud properties for both cases.
Overall, the good agreement between WRF-LES and measurements gives us
confidence to use the LES results to study the AMCI and evaluate reanalysis
for the two CAO events.

Aerosol effects on cloud micro-physical and macro-physical properties (i.e.,
$N_{c}$, and $r_{\rm eff}$, LWP and CFC) are investigated by comparing LES
with aerosol size distributions from different BCB flight legs as input. Our
use of measured aerosol size distributions to study the aerosol effects on
cloud properties better represents aerosol perturbations in the study domain,
which is more realistic compared to other LES studies with prognostic $N_{c}$
but idealized aerosol size distribution. More importantly, LES with the same
configuration and boundary/surface forcings but different aerosol
perturbations allows us to disentangle the aerosol effect on clouds from the
meteorological effect, which is challenging in understanding ACI (Stevens and
Feingold 2009). For the February 28 case, $N_{c}$ and $r_{\rm eff}$ are
influenced by aerosols via aerosol hygroscopicity $\bar{\kappa}$ and aerosol
size distributions. With the same aerosol size distributions, increasing
$\bar{\kappa}$ from 0.313 to 0.392 leads to $5.2\%$ increase ($3.4\%$
decrease) of $N_{c}$ ($r_{\rm eff}$). The top-of-the-atmosphere short wave
radiation $\rm{SW_{TOA}}$ decreases by $1.13\,\rm{W\,m}^{-2}$. LWP (IWP)
increases by $3.2\%$ ($13.1\%$). The CFC only decreases by $0.4\%$. Even
though aerosol size distributions from two BCB legs are quite similar, a
difference of $1.11\,\rm{W\,m}^{-2}$ in $\rm{SW_{TOA}}$ is observed for the
two simulations. For the March 1 case, $\rm{SW_{TOA}}$ only changes by
$0.72\,\rm{W\,m}^{-2}$ when $N_{a}$ differs by a factor of about 2.6 between
two BCB flight legs. The effect of $N_{a}$ on LWP and CFC is negligible.

As we aim to eventually evaluate and improve ACI processes in Earth system
models using LES experiments informed by the ACTIVATE observations, we have
also compared our LES results to satellite retrievals (GOES-16) and reanalysis
products, such as ERA5 and MERRA-2. For the February 28 case, LES and GOES-16
agree reasonably well in LWP and CFC. ERA5 captures the LWP compared with LES
while MERRA-2 slightly underestimates LWP. Time evolution and the magnitude of
CFC among LES, ERA5, and MERRA-2 are quite different. Both ERA5 and MERRA-2
fail to capture the vertical structure of LWC and CFC compared to the LES. For
the March 1 case, LES agree well with GOES-16 in LWP and CFC. Both ERA5 and
MERRA-2 underestimate the LWP compared to LES, even though the time evolution
of LWP exhibit a similar trend between ERA5 and the LES. ERA5 and LES agree
well in the magnitude of CFC while MERRA-2 largely underestimates it. Similar
to the February 28 case, the vertical structure of LWP and CFC from MERRA-2
and ERA5 are quite different from the LES. We have also validated $N_{c}$ and
$r_{\rm eff}$ from the LES against the GOES-16 retrievals. For both cases,
$N_{c}$ and $r_{\rm eff}$ from the LES agrees well with those from GOES-16.

To use the LES results to evaluate AMCI in Earth system models, the next step
will be to simulate these two cases using single-column configuration of Earth
system models driven by the same boundary and surface forcings obtained from
ACTIVATE measurements and reanalysis products.

###### Acknowledgements.

This work was supported through the ACTIVATE Earth Venture Suborbital-3
(EVS-3) investigation, which is funded by NASA’s Earth Science Division and
managed through the Earth System Science Pathfinder Program Office. C.V. and
S.K. thank funding by the DFG within the SPP 1294 HALO and the TRR301-1 TP
change. The Pacific Northwest National Laboratory (PNNL) is operated for the
U.S. Department of Energy by Battelle Memorial Institute under contract DE-
AC05-76RLO1830. The source code used for the simulations of this study, the
Weather Research and Forecasting (WRF) model, is freely available on
https://github.com/wrf-model/WRF. The simulations were performed using
resources available through Research Computing at PNNL. ACTIVATE Data are
publicly available at: http://doi.org/10.5067/SUBORBITAL/ACTIVATE/DATA001

##  Appendix A Validation of log-normal fitting of aerosol size distributions

Table 3: Fitted parameters of the aerosol size distribution for the February 28 case shown in Figure 1. The percentage error (PE) is defined as ${\rm PE}=(\bar{N}_{\rm fit}-\bar{N}_{\rm a})/\bar{N}_{\rm a}\times 100\%$.  BCB leg | Time, UTC | $N\,({\rm cm}^{-3})$ |  $\mu$ (nm) | $\sigma$ | $\bar{N}_{\rm a}\,({\rm cm}^{-3})$ | $\bar{N}_{\rm fit}\,({\rm cm}^{-3})$ | PE
---|---|---|---|---|---|---|---
$N_{1}$ | $N_{2}$ | $N_{3}$ | $\mu_{1}$ | $\mu_{2}$ | $\mu_{3}$ | $\sigma_{1}$ | $\sigma_{2}$ | $\sigma_{3}$
BCB1 | 15:46:53-15:54:54 | 4222 | 994 | 198 | 26.7 | 64.9 | 144.5 | 1.46 | 1.38 | 1.51 | 5593 | 5384 | $-3.7\%$
BCB2 | 16:43:41-16:47:03 | 3757 | 723 | 219 | 33.0 | 63.0 | 173.7 | 1.49 | 1.49 | 1.40 | 5364 | 4690 | $-12.6\%$
Table 4: Fitted parameters of the aerosol size distribution for the March 1 case shown in Figure 2.  BCB leg | Time, UTC | $N\,({\rm cm}^{-3})$ |  $\mu$ (nm) | $\sigma$ | $\bar{N}_{\rm a}\,({\rm cm}^{-3})$ | $\bar{N}_{\rm fit}\,({\rm cm}^{-3})$ | PE
---|---|---|---|---|---|---|---
$N_{1}$ | $N_{2}$ | $N_{3}$ | $\mu_{1}$ | $\mu_{2}$ | $\mu_{3}$ | $\sigma_{1}$ | $\sigma_{2}$ | $\sigma_{3}$
BCB1 | 14:53:22-15:01:45 | 940 | 645 | – | 22.4 | 104.2 | – | 1.51 | 1.47 | – | 1434 | 1479 | $3.1\%$
BCB2 | 15:51:21-15:55:06 | 996 | 1192 | 1118 | 19.0 | 30.2 | 102.3 | 1.49 | 1.31 | 1.51 | 3100 | 3139 | $1.3\%$

The 3-D flight trajectories of the BCB legs for both cases are shown in Figure
15. Figure 16 shows time series of measured particle number concentration of
aerosols (SMPS and LAS) and cloud droplets (FCDP) during the two BCB legs for
both cases. The SMPS measurements are free from spikes, indicative of no
cloud-artifacts (e.g., the cloud shattering), during the measurements. The
validation of the log-normal fitting of aerosol size distributions is
discussed in section 22.1.

\begin{overpic}[width=208.13574pt]{FCDP_traj3D_0228}\put(15.0,70.0){(a)}\end{overpic}\begin{overpic}[width=208.13574pt]{FCDP_traj3D_0301}\put(70.0,70.0){(b)}\end{overpic}

Figure 15: Flight trajectory during the FCDP measurement for (a) the February
28 and (b) March 1 cases. Red and black stars (squares) represent the start
and end of the BCB1 (BCB2) flight leg, respectively. Trajectories with most
dense FCDP-sampling (16.3-16.7 and 15.45-15.75 UTC for the February 28 and
March 1 cases, respectively) are highlighted as thick magenta curves.

\begin{overpic}[width=433.62pt]{CCN_0228}\put(6.5,30.0){(a)}\end{overpic}\begin{overpic}[width=433.62pt]{CCN_0301}\put(6.5,30.0){(b)}\end{overpic}

Figure 16: Comparison between $\bar{N}_{\rm a}$ (black star), $\bar{N}_{\rm fit}$ (black square), and $N_{\rm FCDP}$ (green dots) for (a) the February 28 and (b) March 1 case. Red and blue dots represent $N_{a}$ from SMPS and LAS measurements, respectively.  Table 5: Time-averaged mass concentration $\overline{m_{i}}$ from the AMS measurement sampled during BCB flight legs for the February 28 (0228) and March 1 (0301) cases. NaCl is not efficiently sampled by AMS because it is refractory (i.e., not volatile at 600 Pa), and therefore the Cl mass is likely not representative of NaCl mass. It is justified by the lack of coarse-mode number concentration in Figure 1 and Figure 2.  Component |  | organic | Sulfate (${\rm SO}_{4}^{2-}$) | Nitrate (${\rm NO}_{3}^{-}$) | Ammonium (${\rm NH}_{4}^{+}$)
---|---|---|---|---|---
0228 | BCB1 | $54.5\%$ | $23.4\%$ | $10.8\%$ | $10.0\%$
BCB2 | $48.6\%$ | $25.9\%$ | $10.8\%$ | $13.9\%$
0301 | BCB1 | $27.6\%$ | $46.6\%$ | $3.4\%$ | $21.3\%$
BCB2 | $24.9\%$ | $28.5\%$ | $23.2\%$ | $22.6\%$
Table 6: $\bar{\kappa}$ (time-averaged $\kappa$) calculated according to Equation (2) with AMS-measured $\overline{m_{i}}$ as input listed in Table 5. $\kappa_{i}$ is adopted from Table 1 of Petters and Kreidenweis (2007) for both the non-organic components and the organic one. The mass of ${\rm NH}_{4}^{+}$ is divided to ${\rm(NH_{4})_{2}SO_{4}}$ and ${\rm NH_{4}NO_{3}}$ by its molecular proportion assuming both sulfate and nitrate are fully neutralized as ${\rm(NH_{4})_{2}SO_{4}}$ and ${\rm NH_{4}NO_{3}}$. Taking the upper limit of the kappa value for the organic aerosols as $\kappa_{\rm org}=0.229$ during the BCB1 sampling for the February 28 case, we get $\bar{\kappa}=0.392$.  Component |  | organic | ${\rm(NH_{4})_{2}SO_{4}}$ | ${\rm NH_{4}NO_{3}}$ | $\bar{\kappa}$
---|---|---|---|---|---
$\rho_{i}\,({\rm g\,cm}^{-3})$ |  | 1.35 | 1.77 | 1.72 |
$\kappa_{i}$ |  | 0.1 | 0.61 | 0.67 |
0228 | BCB1 | $54.5\%$ | $30.0\%$ | $14.1\%$ | 0.313
BCB2 | $48.6\%$ | $35.1\%$ | $15.5\%$ | 0.341
0301 | BCB1 | $27.6\%$ | $60.8\%$ | $10.5\%$ | 0.451
BCB2 | $24.9\%$ | $43.5\%$ | $30.7\%$ | 0.479

##  Appendix B Diurnal cycle of cloud properties

Figure 17 shows comparison between the FCDP measurement and LES for the two
cases during the afternoon flights. The corresponding statistics are shown in
Figure 18 and Figure 19 respectively.

\begin{overpic}[width=433.62pt]{FCDP_WRF_comp_L2}\put(-1.0,68.5){(a)}\put(-1.0,34.0){(b)}\end{overpic}
Figure 17: Same as Figure 3 but for the flights (a) from 20:47:07 to 21:10:58
UTC and (b) from 19:43:30 to 20:13:44 UTC for the February 28 and March 1
cases, respectively.

Figure 18: Same as Figure 4 but for the measurements from 20:47:07 to 21:10:58
UTC.

Figure 19: Same as Figure 5 but for the measurements from 19:43:30 to 20:13:44
UTC.

##  Appendix C Ice

Figure 20 shows the vertical profiles of IWC, $\langle N_{\rm ice}\rangle$,
and $\langle r_{\rm eff,ice}\rangle$. Hardly any ice was observed for the
February 28 case. For the March 1 case, $\langle N_{\rm ice}\rangle$ from WRF-
LES agrees well with the 2DS measurement as shown in Figure 21.

Figure 20: Comparison between the WRF-LES and the 2DS measurement of ice
particles. The IWC from WRF-LES only includes ice particles. WRF-LES does not
output $r_{\rm eff,ice}$. The $r_{\rm eff,ice}$ is the largest radius from the
2DS measurement.  Figure 21: Corresponding statistics of Figure 20. 2DS
measurement for the March 1 case for prescribed $N_{a}$. The same criterion
and procedure for the box-and-whisker plot as in Figure 4 are used. The green
stars mark the altitude of flight legs.

##  Appendix D Vertical profiles

Figure 22 and Figure 23 shows the evolution of difference of CFC profiles
between NA and NC simulations for the February 28 and March 1 cases,
respectively.

Figure 22: Evolution of difference of CFC profiles between simulation (a)
$0228\\_\rm{NA1\\_\bar{\kappa}_{org}}$ and 0228$\\_$NC and between (b)
0228$\\_$NA2 and 0228$\\_$NC averaged during the dropsonde measurement time
16:00-17:00 UTC for the February 28 case.  Figure 23: Same as Figure 22 but
for the March 1 case: difference between (a) 0301$\\_$NA1 and 0301$\\_$NC and
between (b) 0301$\\_$NA2 and 0301$\\_$NC averaged over 15:00-16:00 UTC.

Figure 24 shows the vertical profiles of $\theta$, $q_{v}$, $q_{c}$, $u$, $v$,
and $w$ for the February 28 and March 1 cases. Vertical profiles from WRF-LES
reproduce the observed and reanalysis profiles well for both cases. The
dropsonde measurements for the two CAO cases during the ACTIVATE campaign are
described in Li et al. (2021). Figure 25 and Figure 26 show the evolution of
differences of vertical profiles between simulation
$0228\\_\rm{NA1\\_\bar{\kappa}_{org}}$ and $0228\\_{\rm NC}$ and between
simulation $0301\\_{\rm NA}1$ and $0301\\_{\rm NC}$, respectively.

Figure 24: Comparison of vertical profiles among dropsonde measurements (grey
dashed and cyan dotted lines, averaged over all dropsondes during the morning
flight), WRF-LES (blue and red dashed lines, domain averaged), and ERA5
reanalysis (black solid lines, dropsonde center of the morning flight)
averaged during the morning measurement time for the February 28 (upper panel)
and March 1 (lower panel) cases. Dotted lines (with the corresponding colors
for ERA5 and LES) represent the ones for the afternoon flights and only
vertical profiles of NC simulations are shown. 11 and 2 dropsondes are
released for the morning and afternoon flights, respectively. The dropsondes
location of the morning and afternoon flights are slightly different.
Therefore, the vertical profiles between the morning and afternoon flights are
not quantitatively comparable. Same simulations as in Figure 10. See Table 1
for the details of the simulations.  Figure 25: Evolution of differences of
vertical profiles between simulation $0228\\_\rm{NA1\\_\bar{\kappa}_{org}}$
and $0228\\_{\rm NC}$. Same simulations as in Figure 10.  Figure 26: Evolution
of differences of vertical profiles between simulation $0301\\_{\rm NA}1$ and
$0301\\_{\rm NC}$. Same simulations as in Figure 10.

##  Appendix E Retrieve $N_{c}$ and $r_{\rm eff}$ from GOES-16

GOES-16 $N_{c}$ is derived from cloud effective radius in $\mu$m and cloud
optical depth $\tau$ under the adiabatic assumption (Painemal and Zuidema
2011),

$N_{c}=\Gamma^{1/2}\frac{10^{1/2}}{4\pi\rho_{w}^{1/2}k}\frac{\tau^{1/2}}{r_{\rm
eff}^{5/2}},$ (5)

where $\Gamma$ ($\rm{g\,m}^{-4}$) is the the lapse rate due to condensation of
water vapor and is estimated from the cloud top temperature and pressure
retrievals of GOES-16. $\rho_{w}=1000\,\rm{kg\,m}^{-3}$ is the density of
water. $k=r_{v}^{3}/r_{\rm eff}^{3}=0.8$ is assumed to be a constant with
$r_{v}$ the volume mean radius. $N_{c}$ is assumed to be height independent in
Equation (5).

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