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  <front>
    <journal-meta><journal-id journal-id-type="publisher">ACP</journal-id><journal-title-group>
    <journal-title>Atmospheric Chemistry and Physics</journal-title>
    <abbrev-journal-title abbrev-type="publisher">ACP</abbrev-journal-title><abbrev-journal-title abbrev-type="nlm-ta">Atmos. Chem. Phys.</abbrev-journal-title>
  </journal-title-group><issn pub-type="epub">1680-7324</issn><publisher>
    <publisher-name>Copernicus Publications</publisher-name>
    <publisher-loc>Göttingen, Germany</publisher-loc>
  </publisher></journal-meta>
    <article-meta>
      <article-id pub-id-type="doi">10.5194/acp-19-10739-2019</article-id><title-group><article-title>Core and margin in warm convective clouds – Part 2:<?xmltex \hack{\break}?> Aerosol effects
on core properties</article-title><alt-title>Core and margin in warm convective clouds – Part 2</alt-title>
      </title-group><?xmltex \runningtitle{Core and margin in warm convective clouds -- Part 2}?><?xmltex \runningauthor{R. H. Heiblum et al.}?>
      <contrib-group>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Heiblum</surname><given-names>Reuven H.</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Pinto</surname><given-names>Lital</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Altaratz</surname><given-names>Orit</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1 aff2">
          <name><surname>Dagan</surname><given-names>Guy</given-names></name>
          
        <ext-link>https://orcid.org/0000-0002-8391-6334</ext-link></contrib>
        <contrib contrib-type="author" corresp="yes" rid="aff1">
          <name><surname>Koren</surname><given-names>Ilan</given-names></name>
          <email>ilan.koren@weizmann.ac.il</email>
        <ext-link>https://orcid.org/0000-0001-6759-6265</ext-link></contrib>
        <aff id="aff1"><label>1</label><institution>Department of Earth and Planetary Sciences, Weizmann Institute of
Science, Rehovot, Israel</institution>
        </aff>
        <aff id="aff2"><label>a</label><institution>now at: Atmospheric, Oceanic and Planetary Physics, Department of
Physics, University of Oxford, Oxford, UK</institution>
        </aff>
      </contrib-group>
      <author-notes><corresp id="corr1">Ilan Koren (ilan.koren@weizmann.ac.il)</corresp></author-notes><pub-date><day>26</day><month>August</month><year>2019</year></pub-date>
      
      <volume>19</volume>
      <issue>16</issue>
      <fpage>10739</fpage><lpage>10755</lpage>
      <history>
        <date date-type="received"><day>29</day><month>July</month><year>2018</year></date>
           <date date-type="rev-request"><day>30</day><month>August</month><year>2018</year></date>
           <date date-type="rev-recd"><day>10</day><month>June</month><year>2019</year></date>
           <date date-type="accepted"><day>18</day><month>July</month><year>2019</year></date>
      </history>
      <permissions>
        <copyright-statement>Copyright: © 2019 </copyright-statement>
        <copyright-year>2019</copyright-year>
      <license license-type="open-access"><license-p>This work is licensed under the Creative Commons Attribution 4.0 International License. To view a copy of this licence, visit <ext-link ext-link-type="uri" xlink:href="https://creativecommons.org/licenses/by/4.0/">https://creativecommons.org/licenses/by/4.0/</ext-link></license-p></license></permissions><self-uri xlink:href="https://acp.copernicus.org/articles/.html">This article is available from https://acp.copernicus.org/articles/.html</self-uri><self-uri xlink:href="https://acp.copernicus.org/articles/.pdf">The full text article is available as a PDF file from https://acp.copernicus.org/articles/.pdf</self-uri>
      <abstract><title>Abstract</title>
    <p id="d1e125">The effects of aerosol on warm convective cloud cores are evaluated using
single cloud and cloud field simulations. Three core definitions are
examined: positive vertical velocity (<inline-formula><mml:math id="M1" display="inline"><mml:mrow><mml:msub><mml:mi>W</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>), supersaturation
(RH<inline-formula><mml:math id="M2" display="inline"><mml:mrow><mml:msub><mml:mi/><mml:mi mathvariant="normal">core</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, and positive buoyancy (<inline-formula><mml:math id="M3" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>). As presented in Part 1 (Heiblum et al., 2019),
the property <inline-formula><mml:math id="M4" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub><mml:mo>⊆</mml:mo><mml:msub><mml:mi mathvariant="normal">RH</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub><mml:mo>⊆</mml:mo><mml:msub><mml:mi>W</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is
seen during growth of warm convective clouds. We show that this property is
kept irrespective of aerosol concentration. During dissipation core
fractions generally decrease with less overlap between cores. However, for
clouds that develop in low aerosol concentrations capable of producing
precipitation, <inline-formula><mml:math id="M5" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and subsequently <inline-formula><mml:math id="M6" display="inline"><mml:mrow><mml:msub><mml:mi>W</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> volume fractions may
increase during dissipation (i.e., loss of cloud mass). The RH<inline-formula><mml:math id="M7" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:math></inline-formula>
volume fraction decreases during cloud lifetime and shows minor sensitivity
to aerosol concentration.</p>
    <p id="d1e219">It is shown that a <inline-formula><mml:math id="M8" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> forms due to two processes: (i) convective
updrafts – condensation within supersaturated updrafts and release of
latent heat – and (ii) dissipative downdrafts – subsaturated cloudy downdrafts
that warm during descent and “undershoot” the level of neutral buoyancy. The
former process occurs during cloud growth for all aerosol concentrations.
The latter process only occurs for low aerosol concentrations during
dissipation and precipitation stages where large mean drop sizes permit slow
evaporation rates and subsaturation during descent.</p>
    <p id="d1e233">The aerosol effect on the diffusion efficiencies plays a crucial role in the
development of the cloud and its partition to core and margin. Using the
RH<inline-formula><mml:math id="M9" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:math></inline-formula> definition, it is shown that the total cloud mass is mostly
dictated by core processes, while the total cloud volume is mostly dictated
by margin processes. Increase in aerosol concentration increases the core
(mass and volume) due to enhanced condensation but also decreases the margin
due to evaporation. In clean clouds larger droplets evaporate much slower,
enabling preservation of cloud size, and even increase by detrainment and
dilution (volume increases while losing mass). This explains how despite
having smaller cores and less mass, cleaner clouds may live longer and grow
to larger sizes.</p>
  </abstract>
    </article-meta>
  </front>
<body>
      

<sec id="Ch1.S1" sec-type="intro">
  <label>1</label><title>Introduction</title>
      <p id="d1e254">Aerosols remain one of the largest sources of uncertainty in climate
predictions, mainly via their effects on clouds (IPCC, 2013). Here we
focus on the aerosol effects on warm clouds. Aerosols act as cloud
condensation nuclei (CCN) during heterogeneous nucleation of cloud droplets
(Köhler, 1936; Mason and Chien, 1962). The number, size, and composition
of an aerosol distribution determine the initial cloud droplet size
distribution (DSD). Polluted clouds (i.e., more aerosols) have more but
smaller droplets and a narrower DSD compared to clean clouds
(Andreae et al., 2004; Twomey, 1977). Changes
in the initial DSD drive various effects and feedbacks on the cloud's
evolution and key processes, such as droplet mobility,
condensation–evaporation budgets, collision–coalescence, and entrainment
(Jiang et al., 2006; Koren et
al., 2015; Small et al., 2009; Xue and Feingold, 2006).</p>
      <?pagebreak page10740?><p id="d1e257">It is well known that an abundance of small droplets in a cloud (a narrow
DSD) reduces the efficiency of the collision–coalescence process
(Squires, 1958; Twomey, 1977; Warner, 1968),
prolongs the diffusional growth time (Khain et al., 2005;
Wang, 2005), and delays or even completely suppresses the initiation of
precipitation (Albrecht, 1989; Hudson
and Mishra, 2007; Hudson and Yum, 2001; L'Ecuyer et al., 2009). Moreover,
in-cloud condensational growth is more efficient in consuming
supersaturation because of the larger surface-area-to-volume ratio of
droplets (Dagan et
al., 2015a, b; Mordy, 1959; Pinsky et al., 2013; Reutter et al., 2009;
Seiki and Nakajima, 2014). We note that throughout this work the word
<italic>efficient</italic> will be used to describe both the rate and the total change of mass
attributed to a microphysical process. The processes described above enable
the more polluted cloud to condense more water and intensify its growth via
increased release of latent heat (Kogan
and Martin, 1994; Koren et al., 2014; Saleeby et al., 2015; Sheffield et
al., 2015). The smaller droplets are also pushed higher in the atmosphere
due to larger droplet mobility (Koren et al., 2014, 2015).</p>
      <p id="d1e263">However, the increase in aerosol amount yields suppressing effects as well.
An opposite effect should take place in the subsaturated regions of the
cloud, where more numerous and smaller droplets increase the evaporation
rate and loss of cloud mass (Grant and van
den Heever, 2015; Saleeby et al., 2015; Storer and van den Heever, 2013).
Henceforth evaporation will be referred to as a process (i.e., change of mass
per unit of time) rather than complete evaporation of a water drop. Increased
evaporation can promote entrainment mixing, which in turn mixes more subsaturated air into the cloud and further promotes evaporation
(Jiang et al., 2006; Small et al., 2009; Xue and
Feingold, 2006), effectively initiating a positive feedback between
evaporation and mixing with the eventual suppression of cloud growth. This
effect may also be accompanied by a suppressing effect of the larger water
loading in polluted clouds, which contain more liquid water mass.</p>
      <p id="d1e266">The competition between those opposing processes that are driven by enhanced
aerosol loading determines the net aerosol effect on cloud properties such
as cloud fraction, lifetime, albedo, mass, size, and precipitation amount.
However, the sign and magnitude of such effects are non-trivial
(Jiang and Feingold, 2006). Previous studies report opposing findings
regarding the total aerosol effects on warm clouds (Altaratz et
al., 2014). Some studies suggest cloud invigoration by aerosols (bigger and
deeper clouds; Dey
et al., 2011; Kaufman et al., 2005; Koren et al., 2014; Yuan et al., 2011),
while some suggest cloud suppression or no effect at all (Jiang and Feingold,
2006; Li et al., 2011; Savane et al., 2015; Xue et al., 2008). Moreover,
other work has shown that the precipitation susceptibility (i.e., quantifies
the sensitivity of precipitation to the aerosol increase) has a
non-monotonic behavior that reaches its maximum at intermediate liquid water path (LWP) values
(Sorooshian et al., 2009), implying that the resultant aerosol
effects are heavily dependent on cloud type and environmental conditions
(Khain et al., 2008).</p>
      <p id="d1e270">A different approach to aerosol effects suggests that cloud systems can be
buffered to microphysical effects (Stevens and Feingold, 2009).
Several studies have shown that given enough time for the cloud system to
reach steady state, cloud macrophysical parameters (e.g., cloud fraction and
rain yield) show similar results for various aerosol concentrations
(Carrió and Cotton, 2014;
Glassmeier and Lohmann, 2018; Seifert et al., 2015). Based on the idea that
clouds can be partitioned to aerosol-limited, updraft-limited, or aerosol-
and updraft-sensitive regimes (Reutter et al., 2009), a unified theory
for the contradicting results regarding aerosol effects was suggested
(Dagan et al., 2015b). Given an aerosol range that covers all three
regimes, the competition between opposite processes leads to an optimum
value of aerosol concentration regarding various cloud properties like total
mass, cloud top, or rain (Dagan et al., 2015b). A cloud that develops under
low aerosol concentration is aerosol limited, as it does not have enough
collective droplet surface area to consume the available water vapor. On the
other side of the trend, a cloud that develops in polluted environment (with
more aerosols than the optimum) is influenced significantly by enhanced
entrainment and larger water loading, causing suppression of cloud
development. The optimal concentration is a function of the thermodynamic
conditions (temperature and humidity profiles) and cloud size.</p>
      <p id="d1e273">Environments that support larger cloud development will have larger cloud
cores that are positively affected by aerosol increase and can be regarded
as aerosol limited (i.e., on the ascending branch of the aerosol trend) up to
a higher optimal aerosol concentration. Environmental conditions that
support small clouds are more strongly affected by cloud suppression
processes at the cloud margins (due to higher cloud surface-area-to-volume
ratio) and would have a lower optimal aerosol concentration. This can
explain why studies biased to smaller clouds (mostly numerical modeling
studies) report cloud suppression and studies biased to larger clouds
(mostly observational studies) report cloud invigoration. Similar
conclusions were reached for the cloud field scale as well (Dagan et al.,
2017).</p>
      <p id="d1e276">In addition, it was shown that clouds impact differently the environmental
thermodynamics according to the aerosol level in the field
(Dagan et al., 2016; Seifert and
Heus, 2013; Seifert et al., 2015). For example changes in aerosol loading
impact the amount of precipitation reaching the surface and subsequently the
evaporative cooling below cloud base and the organization patterns
(Seifert and Heus, 2013; Seigel,
2014; Xue et al., 2008). Moreover, an increase in aerosol loading may
increase evaporation rates around the margins and tops of clouds
(Seigel, 2014; Stevens, 2007;
Xue and Feingold, 2006), cooling the upper cloudy layer and increasing the
convective instability. Therefore aerosol effects on phase changes and
precipitation result in vertical redistribution of heat and moisture, which
may either stabilize or destabilize the environment in which subsequent
clouds grow (Seifert and Heus, 2013).</p>
      <?pagebreak page10741?><p id="d1e279">Irrespective of the definition chosen, the cloud's core and margin are
dominated by different processes (Dagan et al., 2015b). These processes
often compete with each other, with the dominant one changing along the
cloud's evolution. For example, at the initial stage of cloud formation, a
cloud is more adiabatic and is controlled by the core's processes
(condensation), and when it dissipates the margin processes are more
dominant (entrainment and evaporation). Aerosols affect each of these
processes and thus each stage in the cloud's lifetime. As a continuation of
Part 1 (Heiblum et al., 2019) of this work (hereafter PT1), in this part we analyze aerosol
effects on the cloud's partition to core and margin throughout the lifetime
of a cloud. We report the consequences that these effects have on evolution of a
cloud in terms of volume, mass, and lifetime. As opposed to other works
that typically focus on a single cloud core definition, here three different
definitions are used (see Sect. 2), with emphasis placed on the sensitivity of
each core definition to aerosol concentration. Moreover, the combination of
single cloud with large-eddy simulations enables us to gain process-level
understanding and test the robustness of our findings.</p>
</sec>
<sec id="Ch1.S2">
  <label>2</label><title>Methods</title>
      <p id="d1e290">The analyses performed here are to the most part identical to those
described in PT1 of this work. In this section we shall thus only give a
brief review of the methods used. For single cloud simulations we use the
Tel Aviv University axisymmetric cloud model (TAU-CM; Reisin et
al., 1996), and for cloud field simulations we use the System for
Atmospheric Modeling (SAM) model (version 6.10.3; for details see the following web page:
<uri>http://rossby.msrc.sunysb.edu/~marat/SAM.html</uri>, last access: 10 October 2018; Khairoutdinov and Randall, 2003).</p>
      <p id="d1e296">Both models utilize explicit bin-microphysics schemes
(Khain et al., 2004; Tzivion et al., 1987), solving
nucleation, diffusion (i.e., condensation and evaporation), collisional
coalescence, breakup, and sedimentation microphysical processes. The single
cloud model is initialized using a Hawaiian thermodynamic profile based on
the 91285 PHTO Hilo radiosonde at 00:00 Z on 21 August 2007. The cloud field model
is set up based on the BOMEX case study, including an initialization setup
(sounding, surface fluxes, and surface roughness) and large-scale forcing
setup (Siebesma et al., 2003). More details on the model
setups and definitions can be found in PT1.</p>
      <p id="d1e299">To study the effects of aerosols on the cloud cores we run each model setup
with three different aerosol concentrations: clean – 25 cm<inline-formula><mml:math id="M10" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>,
intermediate – 250 cm<inline-formula><mml:math id="M11" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>, and polluted – 2000 cm<inline-formula><mml:math id="M12" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>. The model
domain is initialized using an oceanic size distribution (Altaratz et
al., 2008; Jaenicke, 1988), maintaining a constant mixing ratio with height.
The aerosol budget includes removal by nucleation and regeneration upon
evaporation, while wet scavenging by precipitation removes aerosols from the
domain. Thus, the aerosol concentration may be depleted by
20 %–40 % (depending on the precipitation amount) during the
simulation. More on the treatment of aerosols in the cloud field model can
be found in previous work (Heiblum et al., 2016a). As defined
in PT1, all pixels with at least 0.01 g kg<inline-formula><mml:math id="M13" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> of liquid water are
considered cloudy. Cloud cores are defined using three definitions: (1) RH<inline-formula><mml:math id="M14" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:math></inline-formula> : relative humidity <inline-formula><mml:math id="M15" display="inline"><mml:mrow><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">100</mml:mn></mml:mrow></mml:math></inline-formula> %, (2) <inline-formula><mml:math id="M16" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> : buoyancy
<inline-formula><mml:math id="M17" display="inline"><mml:mrow><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:math></inline-formula>, and (3) <inline-formula><mml:math id="M18" display="inline"><mml:mrow><mml:msub><mml:mi>W</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> : vertical velocity <inline-formula><mml:math id="M19" display="inline"><mml:mrow><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:math></inline-formula>. Relative
humidity (RH) and vertical velocity (<inline-formula><mml:math id="M20" display="inline"><mml:mi>W</mml:mi></mml:math></inline-formula>) are standard outputs of the model,
while the buoyancy (<inline-formula><mml:math id="M21" display="inline"><mml:mi>B</mml:mi></mml:math></inline-formula>) is calculated based on Eq. (1) in PT1, where each
cloudy pixel is compared with the mean non-cloudy thermodynamic reference
state per height.</p>
      <p id="d1e427">In order to reduce the problem's dimensionality and distill signals in a
cloud field system governed by high variance, we use the center of gravity vs. mass
(CvM) phase space in combination with an automated 3-D cloud tracking
algorithm (Heiblum et al., 2016a). The CvM phase space enables
a compact view of all clouds in the simulation by projecting only their
center-of-gravity (COG) height and mass at each output time step. Using the
cloud tracking, it was shown that the lifetime of a cloud can be described
by a trajectory on this phase space. Hence, the different locations in the
CvM space are associated with different stages in a cloud's lifetime (i.e., growing, precipitating, and dissipating). For an in-depth explanation of the
CvM space, the reader is referred to Sect. 2.4 in PT1 (see schematic
illustration – Fig. 1, PT1).</p>
</sec>
<sec id="Ch1.S3">
  <label>3</label><title>Results – single cloud simulations</title>
<sec id="Ch1.S3.SS1">
  <label>3.1</label><title>Sensitivity of different core types to aerosol concentration</title>
      <p id="d1e445">Figure 1 presents time series of single cloud core volume fractions
(<inline-formula><mml:math id="M22" display="inline"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mi mathvariant="normal">vol</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) and cores' properties for three aerosol concentrations (clean,
intermediate, and polluted). Also included are time series of instantaneous
rain rates (mm h<inline-formula><mml:math id="M23" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>) at the domain surface. For all aerosol
concentrations and during most of the clouds' lifetimes, the volume fraction
of <inline-formula><mml:math id="M24" display="inline"><mml:mrow><mml:msub><mml:mi>W</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> tends to be the largest and the volume fraction of <inline-formula><mml:math id="M25" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> the smallest.
Exceptions to this finding are seen either at the initial time step for the
polluted cloud or in the later stages of cloud lifetime for the lower-concentration clouds. In addition, we find that <inline-formula><mml:math id="M26" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">RH</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub><mml:mo>⊆</mml:mo><mml:msub><mml:mi>W</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> for all stages of cloud lifetime while <inline-formula><mml:math id="M27" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub><mml:mo>⊆</mml:mo><mml:msub><mml:mi>W</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M28" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">RH</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> for all stages of the polluted cloud, but this only applies
to the growing stages of lower-concentration clouds before precipitation
production. Thus, the main finding from PT1 (i.e., <inline-formula><mml:math id="M29" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub><mml:mo>⊆</mml:mo><mml:msub><mml:mi mathvariant="normal">RH</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub><mml:mo>⊆</mml:mo><mml:msub><mml:mi>W</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) generally applies to all aerosol
concentrations during the pre-precipitation stages of the clouds' lifetimes.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F1" specific-use="star"><?xmltex \currentcnt{1}?><label>Figure 1</label><caption><p id="d1e568"><bold>(a, c, e)</bold> Time series of core volume fractions (<inline-formula><mml:math id="M30" display="inline"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mi mathvariant="normal">vol</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> in %;
left axis) and surface rain rate (<inline-formula><mml:math id="M31" display="inline"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mi mathvariant="normal">surf</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> in mm h<inline-formula><mml:math id="M32" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>; right axis)
for the clean <bold>(a)</bold>, intermediate <bold>(c)</bold>, and polluted <bold>(e)</bold> single cloud
simulations. <bold>(b, d, f)</bold> Time series of pixel fractions (<inline-formula><mml:math id="M33" display="inline"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mi mathvariant="normal">pixel</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> in %) of
one core type within another, for the respective simulation types.
Core volume and pixel fractions are indicated by different line colors (see
legends).</p></caption>
          <?xmltex \igopts{width=398.338583pt}?><graphic xlink:href="https://acp.copernicus.org/articles/19/10739/2019/acp-19-10739-2019-f01.png"/>

        </fig>

      <p id="d1e637">Lower-aerosol-concentration simulations produce more rain and at earlier
stages of cloud lifetime due to efficient collision coalescence. The
increase in the <inline-formula><mml:math id="M34" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> volume fraction at later stages of cloud lifetime in
those simulations (clean and intermediate) coincides with initiation of
precipitation production followed by a consequent increase in the <inline-formula><mml:math id="M35" display="inline"><mml:mrow><mml:msub><mml:mi>W</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>
volume fraction as well (more so for the intermediate concentration). This
dissipating <inline-formula><mml:math id="M36" display="inline"><mml:mrow><mml:msub><mml:mi>W</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is mostly contained within the <inline-formula><mml:math id="M37" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>. The possible
mechanism behind the increase in<?pagebreak page10742?> prevalence of buoyant parcels during
precipitation is explored in Sect. 3.2. The lack of RH<inline-formula><mml:math id="M38" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:math></inline-formula> pixels at
these stages indicates that the <inline-formula><mml:math id="M39" display="inline"><mml:mrow><mml:msub><mml:mi>W</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is composed of pixels with small
vertical velocities, insufficient for supersaturation production. The
RH<inline-formula><mml:math id="M40" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:math></inline-formula> is the only one which is not sensitive to rain and monotonically
decreases during all clouds' lifetimes. Another clear aerosol effect seen in
Fig. 1 is an increase in cloud lifetime with a decrease in aerosol
concentration. This point will be further explored in Sect. 3.3.</p>
</sec>
<sec id="Ch1.S3.SS2">
  <label>3.2</label><title>Mechanisms governing positive buoyancy</title>
      <p id="d1e722">The theoretical arguments in PT1 showed that <inline-formula><mml:math id="M41" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> should be the
smallest of the three. This was shown for both the adiabatic cloud column
case and also the non-adiabatic case, where entrainment mixing and consequent
evaporation have a strong net negative effect on cloud buoyancy. Despite
this fact, results show (see Fig. 1 and Fig. 2 in PT1) that pockets of
positive buoyancy may form independently of the other cores during dissipation
and precipitation stages, even though evaporation is to be expected then.
Since positive buoyancy is the result of either higher temperature or vapor
content (or both) than the surrounding environment, we choose to analyze
these two terms during different stages of the single clouds' lifetimes. The
liquid water content (LWC) buoyancy term (not shown here) is always negative and
typically increases (in absolute value) with an increase in vertical velocity
or total buoyancy.</p>
      <p id="d1e736"><?xmltex \hack{\newpage}?>Figure 2 shows the values of the temperature (<inline-formula><mml:math id="M42" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) and humidity
(<inline-formula><mml:math id="M43" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">Qv</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) buoyancy terms in pixel buoyancy vs. pixel vertical velocity
phase space. The scatterplots include all cloudy pixels during all time
steps for the three different aerosol concentration simulations. The
distribution of points for the polluted simulation shows a positive linear
dependence of buoyancy on vertical velocity. Negative vertical velocity is
associated with negative buoyancy, and positive vertical velocity shows a
transition from negative to positive buoyancy with an increase in magnitude.
For this case both <inline-formula><mml:math id="M44" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M45" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">Qv</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> increase with an increase in vertical
velocity, as is generally expected in convective clouds. The sign of pixel
buoyancy is mostly dependent on <inline-formula><mml:math id="M46" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, since all pixels have positive
<inline-formula><mml:math id="M47" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">Qv</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and a negative water loading term. This behavior is also seen for
lower aerosol concentrations, where the sign of buoyancy is for the most part
determined by <inline-formula><mml:math id="M48" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>. Hereafter, we refer to positive buoyancy (both
<inline-formula><mml:math id="M49" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M50" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">Qv</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) production within updrafts as updraft buoyancy.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F2" specific-use="star"><?xmltex \currentcnt{2}?><label>Figure 2</label><caption><p id="d1e842">Scatterplots of pixel total buoyancy (m s<inline-formula><mml:math id="M51" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>) vs. pixel
vertical velocity (m s<inline-formula><mml:math id="M52" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>) for the clean <bold>(a, d)</bold>, intermediate <bold>(b, e)</bold>, and
polluted <bold>(c, f)</bold> simulations. Data include all cloudy pixels during all time
steps. Colors represent magnitude of buoyancy temperature term (<inline-formula><mml:math id="M53" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>;
<bold>a, b, c</bold>) and humidity term (<inline-formula><mml:math id="M54" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">Qv</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>; <bold>d, e, f</bold>), where red (blue) shades indicate
positive (negative) values. Markers with superimposed black dots represent
temporal stages with non-zero surface precipitation. White arrows indicate
outlier scatter of pixels with positive buoyancy and negative vertical
velocity.</p></caption>
          <?xmltex \igopts{width=441.017717pt}?><graphic xlink:href="https://acp.copernicus.org/articles/19/10739/2019/acp-19-10739-2019-f02.png"/>

        </fig>

      <p id="d1e914">The clean and intermediate simulations show a similar dependence of buoyancy
on vertical velocity; however, it is apparent that these simulations also
include an outlier scatter region of pixels with positive buoyancy and weak
negative vertical velocity which is absent in the polluted simulation (see
white arrows; Fig. 2). Consistent with the rest of the cloudy pixels, these
outlier pixels have positive <inline-formula><mml:math id="M55" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> but differ in that they show neutral
<inline-formula><mml:math id="M56" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">Qv</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>. It can also be seen that these pixels are only attributed to the
stages after surface precipitation has commenced (indicated by black dots in
markers). Precipitation is indicative of both downdraft motion and abundance
of large drop sizes.</p>
      <?pagebreak page10743?><p id="d1e939">Although not usually the focus of studies, the existence of positively
buoyant downdrafts in convective clouds has been reported in both
observations (Igau et al., 1999; Wei et al., 1998)
and simulations (Xu and Randall, 2001; Zhao
and Austin, 2005a, b). A possible explanation for this can be deduced
from previous theoretical studies predicting mixing-induced downdrafts in
cumulus clouds (Betts and Silva Dias, 1979; Betts,
1982). It was shown that in some cases cloud–environment mixtures are
negatively buoyant (while still containing liquid water), and the consequent
downdrafts can sometimes descend only partway down to the cloud base before
reaching neutral buoyancy. Similar to convective overshooting, parcels with
negative vertical momentum may then undershoot the downdraft equilibrium
level and turn positively buoyant while the downdraft weakens. One can
therefore expect the magnitude of positive buoyancy within the downdraft to
reach a maximum when the velocity approaches zero. Hereafter we refer to
positive buoyancy production within downdrafts as downdraft buoyancy.</p>
      <p id="d1e942">Downdraft buoyancy production occurs frequently in cumulus fields because
the negatively buoyant downdrafts follow a warming lapse rate which is more
unstable than the environmental one, which is typically between the dry
adiabat and moist adiabat (as is the case for the Hawaiian and BOMEX
profiles simulated in this work). On one extreme, a descending parcel is
least buoyant (i.e., coolest) when evaporation (after mixing) keeps it just
barely saturated (Paluch and Breed, 1984, also PT1) so that the
lapse rate of descent tends to be moist adiabatic and may remain negatively
buoyant. On the other extreme, if little to no evaporation of liquid water
occurs, the descent will follow the dry adiabat and switch to neutral (and
then positive) buoyancy rapidly. Thus, the ability of a negatively buoyant
cloudy downdraft to sustain itself depends on continuous inflow of liquid
water (by mixing) and its consequent evaporation (Knupp and Cotton,
1985).</p>
      <p id="d1e945">Indeed, the results in Fig. 2 match the hypothesis explained above, where
positively buoyant downdrafts are warmer than the environment and tend to
show larger buoyancy values for weaker downdraft velocities (especially for
the intermediate case). Further analysis also shows that the more
unsaturated the downdrafts (indicated also by low <inline-formula><mml:math id="M57" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">Qv</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>), the larger the
positive buoyancy. Moreover, the occurrence during precipitating stages and
for lower aerosol concentrations indicates that slow evaporation due to
larger drop sizes is crucial for downdraft buoyancy production, enabling a
near-dry adiabatic lapse rate during descent.</p>
</sec>
<sec id="Ch1.S3.SS3">
  <label>3.3</label><title>The dependency of cloud characteristics on core and margin's processes</title>
      <p id="d1e967">Here we evaluate how aerosol effects within the core and margin (using the
three core definitions) affect the cloud characteristics, focusing on two
main parameters: size (or volume) and mass. In Fig. 3 we follow the
evolution of cloud, core, and margin mass and volume for different aerosol
concentrations, using only the RH<inline-formula><mml:math id="M58" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:math></inline-formula> definition. We choose the
RH<inline-formula><mml:math id="M59" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:math></inline-formula>, since it is the most stable out the core types,<?pagebreak page10744?> generally
decreasing monotonically (see Fig. 1). A non-monotonic dependency of total
cloud mass on aerosol concentration is seen, showing a maximum for the
intermediate concentration. This type of dependency has been previously
reported for warm cumulus clouds (Dagan et al., 2015b; Savane et al.,
2015).</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F3" specific-use="star"><?xmltex \currentcnt{3}?><label>Figure 3</label><caption><p id="d1e990">Time series of cloud mass (kg; <bold>a, c, e, g</bold>) and cloud volume
(km<inline-formula><mml:math id="M60" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:math></inline-formula>; <bold>b, d, f, h</bold>) for the different aerosol concentrations simulations
(see legend). The total <bold>(a, b)</bold>, core <bold>(c, d)</bold>, margin <bold>(e, f)</bold>, and relative
fraction <bold>(g, h)</bold> values are shown for each parameter, as indicated by panel
titles. The core here is defined according to RH <inline-formula><mml:math id="M61" display="inline"><mml:mo>&gt;</mml:mo></mml:math></inline-formula> 100 %
definition.</p></caption>
          <?xmltex \igopts{width=398.338583pt}?><graphic xlink:href="https://acp.copernicus.org/articles/19/10739/2019/acp-19-10739-2019-f03.png"/>

        </fig>

      <p id="d1e1034">One can generally expect an increase in diffusion and decrease in
collision–coalescence processes efficiency with an increase in aerosol
concentration (Hudson and Yum, 2001;
Jiang et al., 2009; L'Ecuyer et al., 2009; Pinsky et al., 2013), affecting
both condensation and evaporation processes. The intermediate concentration
shows the highest total mass as a result of being an optimal case, with
higher condensation efficiency than the clean case and lower evaporation
efficiency than the polluted case. It is convenient to represent the
condensation and evaporation efficiencies by the RH<inline-formula><mml:math id="M62" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:math></inline-formula> and
RH<inline-formula><mml:math id="M63" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">margin</mml:mi></mml:msub></mml:math></inline-formula> mass, respectively. The intermediate cloud has almost
identical core mass as the polluted cloud but retains higher mass in
its margin as well. The clean cloud shows the lowest core mass but manages
to accumulate the largest mass in its margin that dissipates slowly in
subsaturated conditions. By comparing the total cloud mass evolution with
the core and margin mass evolutions, it becomes clear that the total mass is
primarily dependent on the cloud core. Another way to see this is by
plotting the core mass fraction (Fig. 3g), which shows that
clouds are core dominated (core fraction <inline-formula><mml:math id="M64" display="inline"><mml:mrow><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">0.5</mml:mn></mml:mrow></mml:math></inline-formula>) with respect to
mass for most of their lifetimes and for all aerosol concentrations.</p>
      <p id="d1e1066">With respect to cloud total volume, the lower the concentration, the larger
the total cloud volume. We note that the cloud volume here excludes regions
of precipitation below the initial cloud base height. By separating to core
and margin regions, one can see that the total cloud volume is primarily
dependent on the volume of the margin, which increases significantly with
decreasing concentration. This is especially true during the dissipating
stages of cloud lifetime, when the cloud is margin dominated. Although
increasing the aerosol concentration does initially yield an increase in
core volume (as was seen for the mass), the extents of the core size are
typically smaller than those of the margin. There are large differences in
the relative core volume percentage for the different clouds. The clean
(polluted) cloud is margin (core) dominated with respect to volume for most
of its lifetime. Excluding time of formation, the clean cloud shows the
lowest core volume fractions but manages to maintain its core for the
longest time span.</p>
      <p id="d1e1069">These results with respect to cloud volume can be attributed to the smaller
drop sizes and higher diffusion efficiencies with an increase in aerosol
concentration. Additionally, lower collision–coalescence efficiencies also
maintain a narrow droplet spectrum of small droplets in the polluted cloud.
During the growing stage a higher aerosol concentration may permit the cloud
to condense more water, release more latent heat, and promote cloud growth.
This explains the larger core volume sizes. However, after the cloud
exhausts its convective potential (i.e., the growth of the convective core
terminates and reaches its peak in mass), its main method of expansion is by
mixing with the environment (i.e., detrainment and dilution). We note that
precipitation can also be considered a method of expansion; however our
choice to focus on volume above initial cloud base excludes this effect.
Detrainment and mixing with the environment result in subsaturation
conditions and evaporation of LWC. A clear indication for dilution is seen
in Fig. 3, where between 30 and 35 min of simulation time, both the clean and
polluted clouds lose total mass but only the clean cloud increases in total
volume. The polluted cloud is composed of small drops, evaporates its margin
regions efficiently, and is thus limited in horizontal growth by
detrainment. The clean cloud is composed of larger drops, less efficient in
evaporating its margins, and hence can grow by dilution of its LWC upon a
larger volume. This large margin “shields” the core during dissipation
stages and enables it to the live for a longer time.</p>
      <p id="d1e1072">The mechanism behind the results in Fig. 3 is demonstrated in Fig. 4, where
horizontal cross-sections of mean (taken in the vertical dimension) cloud RH
are shown for different stages during the clouds' lifetimes. For the
polluted cloud, supersaturated or subsaturated conditions are rare. The RH
throughout the cloud is near 100 % (almost always between 99.8 % and
100.2 %) except for a few pixels at its far edges which are a bit below
99 %. The polluted cloud resembles what one would expect to see using a
moist adiabatic approximation (i.e., saturation adjustment), where all excess
water vapor above saturation is converted to liquid water, mimicking
infinitely efficient condensation (and evaporation).</p>

      <?xmltex \floatpos{p}?><fig id="Ch1.F4"><?xmltex \currentcnt{4}?><label>Figure 4</label><caption><p id="d1e1077">Four snapshots of horizontal cross-sections of RH (%; see
panel titles for times). Panels include the results of different aerosol
concentrations (see legend). Cross-sections are obtained by taking the mean
RH of all vertical levels for each horizontal distance from the cloud center
axis.</p></caption>
          <?xmltex \igopts{width=199.169291pt}?><graphic xlink:href="https://acp.copernicus.org/articles/19/10739/2019/acp-19-10739-2019-f04.png"/>

        </fig>

      <p id="d1e1086">The clean cloud shows opposite behavior, with extremes of large
supersaturation during cloud growth (initial stages) and large
subsaturation during cloud dissipation (final stages). The large
supersaturation can be explained by slow diffusional growth, but the large
subsaturation also takes into consideration the larger drop sizes, which
take more time to evaporate. This enables the clean cloud to expand
to larger horizontal extents (by dilution and mixing with the environment
without fully evaporating) and live for longer times. The intermediate
aerosol concentration shows a midway scenario, where the supersaturation is
consumed more efficiently than the clean case and at the same time much
larger values of subsaturation may exist than those seen for the polluted
case.</p>
</sec>
</sec>
<sec id="Ch1.S4">
  <label>4</label><title>Results – cloud field simulations</title>
      <p id="d1e1098">In the following section we expand our analyses of aerosol effects on cloud
core and margin from the single cloud scale to the cloud field scale. A
cloud field can be considered to be composed of many individual clouds and thus
can serve<?pagebreak page10745?> to test the robustness of the aerosol effects seen for a single
cloud. Moreover, cloud fields include the added complexity of interactions
between clouds and the clouds' effects on their thermodynamic environment.</p>
<sec id="Ch1.S4.SS1">
  <label>4.1</label><title>Sensitivity of different core types to aerosol concentration</title>
      <p id="d1e1108">Here CvM space representations (see Sect. 2) are used to observe the core
volume fractions of all clouds in BOMEX cloud field simulations. The rows in
Fig. 5 represent different aerosol concentrations, while the columns
represent different core type definitions. Different aerosol concentrations
produce a vastly different scatter of clouds in the CvM space, as was
previously discussed in depth (Heiblum et al., 2016b). The
clean simulation (25 cm<inline-formula><mml:math id="M65" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>) shows two disconnected regions of cloud
scatter: one which is adjacent to the adiabatic approximation and one of
mainly small mass and high-COG clouds. The former region includes both
clouds during their growth stages (smaller masses, LWP <inline-formula><mml:math id="M66" display="inline"><mml:mo>&lt;</mml:mo></mml:math></inline-formula> 10 g m<inline-formula><mml:math id="M67" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>) and large precipitating entities (larger masses, LWP <inline-formula><mml:math id="M68" display="inline"><mml:mo>&gt;</mml:mo></mml:math></inline-formula> 10 g m<inline-formula><mml:math id="M69" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>) which form due to merging processes (Heiblum et
al., 2016b). The latter region (small mass and high COG) includes clouds at
their dissipating stage, which form by the shedding mechanism off the large
cloud entities. We note also the existence of small-mass elements well below
the adiabat, representing precipitation cloud segments which shed off large
precipitating clouds.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F5" specific-use="star"><?xmltex \currentcnt{5}?><label>Figure 5</label><caption><p id="d1e1163">CvM phase-space diagrams of <inline-formula><mml:math id="M70" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> <bold>(a, d, g)</bold>, RH<inline-formula><mml:math id="M71" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:math></inline-formula> <bold>(b, e, h)</bold>, and <inline-formula><mml:math id="M72" display="inline"><mml:mrow><mml:msub><mml:mi>W</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> <bold>(c, f, i)</bold> volume fractions (<inline-formula><mml:math id="M73" display="inline"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mi mathvariant="normal">vol</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) for all clouds
between 3  and 8 h in the BOMEX simulations. The rows correspond to the
clean <bold>(a, b, c)</bold>, intermediate <bold>(d, e, f)</bold>, and polluted <bold>(g, h, i)</bold> aerosol cases. The
red (blue) colors indicate a core <inline-formula><mml:math id="M74" display="inline"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mi mathvariant="normal">vol</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> above (below) 0.5. The size of
each point in the scatter is proportional to the cloud mean area, where the
smallest (largest) point corresponds to an area of 0.01 km<inline-formula><mml:math id="M75" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:math></inline-formula> (11.4 km<inline-formula><mml:math id="M76" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:math></inline-formula>). The
percentage of clouds that are core dominated
(<inline-formula><mml:math id="M77" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">f</mml:mi><mml:mi mathvariant="normal">vol</mml:mi></mml:msub><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">0.5</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> is included in panel legends. For
an in-depth description of CvM space characteristics, the reader is referred
to Sect. 2.4 in PT1.</p></caption>
          <?xmltex \igopts{width=441.017717pt}?><graphic xlink:href="https://acp.copernicus.org/articles/19/10739/2019/acp-19-10739-2019-f05.png"/>

        </fig>

      <p id="d1e1280">The polluted simulation (2000 cm<inline-formula><mml:math id="M78" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>) shows a much more homogeneous
scatter of clouds. The lower part of the scatter (closest to the adiabat)
represents the cloud growing branch,<?pagebreak page10746?> while the rest of the scatter represents
dissipating clouds, either by the gradual process of rising cloud base or by
an immediate process of shedding off larger cloud entity (see Fig. 1, PT1).
Precipitating cloud segments below the adiabat are absent from this
simulation. The intermediate simulation (250 cm<inline-formula><mml:math id="M79" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>) shows a scatter
which generally resembles the polluted case. However, the existence of
relatively disconnected (from the main cloud scatter) small-mass cloud
segments below the adiabat and near the inversion base height resembles the
clean simulation as well. It should be noted that horizontal dashed lines in
Fig. 5 represent the inversion base height after 5 h of simulation
(approximately middle of simulation), where an increase in the inversion
base height is seen with a decrease in aerosol concentration. This is due to
increased net warming in the upper cloudy layer (i.e., release of latent
heat during condensation with reduced local evaporation) with an increase in
precipitation (Dagan et al.,
2016; Heiblum et al., 2016b), which raises the inversion base.</p>
      <p id="d1e1308">The results in Fig. 5 show a consistent behavior of the core volume
fractions for all aerosol concentrations, where the <inline-formula><mml:math id="M80" display="inline"><mml:mrow><mml:msub><mml:mi>W</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> type shows the
largest fractions and the <inline-formula><mml:math id="M81" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> type shows the smallest fractions. The
<inline-formula><mml:math id="M82" display="inline"><mml:mrow><mml:msub><mml:mi>W</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and RH<inline-formula><mml:math id="M83" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:math></inline-formula> generally show a decrease in core fractions along
the growing branch, while the <inline-formula><mml:math id="M84" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> fraction initially increases with
cloud growth and then decreases for the large-mass growing clouds. The
percentages in the panel legends (Fig. 5) indicate the fraction of clouds
(out of the scatter) which are core dominated with respect to volume
(<inline-formula><mml:math id="M85" display="inline"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mi mathvariant="normal">vol</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M86" display="inline"><mml:mo>&gt;</mml:mo></mml:math></inline-formula> 0.5). For all concentrations, less than 7 % of
clouds are <inline-formula><mml:math id="M87" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> dominated, while more than 55 % are <inline-formula><mml:math id="M88" display="inline"><mml:mrow><mml:msub><mml:mi>W</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>
dominated (with RH<inline-formula><mml:math id="M89" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:math></inline-formula> percentages somewhere in between). The
<inline-formula><mml:math id="M90" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> typically occupies a small portion of a typical cloud volume, while
the <inline-formula><mml:math id="M91" display="inline"><mml:mrow><mml:msub><mml:mi>W</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> typically occupies most of the cloud. The mean cloud area
(proportional to scatter point size) shows an increase with the increase in mean
cloud LWP.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F6" specific-use="star"><?xmltex \currentcnt{6}?><label>Figure 6</label><caption><p id="d1e1439">Average core mass fraction <bold>(a)</bold> and volume fraction <bold>(b)</bold> values for
different aerosol concentrations, as indicated in the legend. The average
only includes growing branch clouds from within the CvM space (i.e., clouds
located in proximity to the adiabat). The core here is defined according to
RH <inline-formula><mml:math id="M92" display="inline"><mml:mo>&gt;</mml:mo></mml:math></inline-formula> 100 % definition.</p></caption>
          <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://acp.copernicus.org/articles/19/10739/2019/acp-19-10739-2019-f06.png"/>

        </fig>

      <p id="d1e1461">These results are consistent with PT1 and the single cloud simulations in
Sect. 3.1. Nevertheless, some significant aerosol effects on the partition
to core types can be seen. Focusing on the growing branch first (i.e., clouds
located near the adiabat), we note the following:
<list list-type="order"><list-item>
      <p id="d1e1466">For the RH<inline-formula><mml:math id="M93" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:math></inline-formula> type, the core volume fractions of clouds after formation (i.e., with small mass) increase with decreasing aerosol concentration. This effect was also seen for the single cloud simulations and can be explained by the reduced efficiency of supersaturation consumption for fewer aerosols.</p></list-item><list-item>
      <p id="d1e1479">The <inline-formula><mml:math id="M94" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> volume fraction increases at smaller mass values (or earlier in cloud's lifetime) and to higher values for increasing aerosol concentration. This effect is complementary to the previous one, since efficient consumption of supersaturation should result in more latent heat release and positive buoyancy.</p></list-item><list-item>
      <p id="d1e1494">The core volume fractions of the largest mass clouds increase with increasing aerosol concentration for all core types.</p></list-item><list-item>
      <p id="d1e1498">The mean area of large-mass clouds increases significantly with a decrease in aerosol concentration.</p></list-item></list>
We also note a general increase in the fraction of clouds that are
<inline-formula><mml:math id="M95" display="inline"><mml:mrow><mml:msub><mml:mi>W</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> or RH<inline-formula><mml:math id="M96" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:math></inline-formula> dominated with an increase in aerosol concentration,
meaning adding aerosols shift a cloud from being mostly margin to being
mostly core. The <inline-formula><mml:math id="M97" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is an exception, since the clean case shows the
highest fraction of <inline-formula><mml:math id="M98" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>-dominated clouds, and both the clean and
polluted cases are more <inline-formula><mml:math id="M99" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> dominated than the intermediate case. This
can be explained by the different mechanisms of buoyancy production (see
Sects. 3.2 and 4.2), where the polluted case is positively influenced by
updraft buoyancy production and a larger core volume fraction, while the
frequently precipitating clean case is positively influenced by downdraft
buoyancy production. For the dissipating branch clouds, a highly variable
pattern of core volume fractions can be seen, especially for the small-mass
clouds. For all aerosol concentrations, these small cloud fragments can be
either core dominated, margin dominated, or equally partitioned. One can
assume that these differences can be related to the different mechanisms by
which cloud fragments form, either by gradual dissipation of a large cloud
or by instantaneous shedding of a large cloud. As for aerosol effects on
the dissipating clouds, we see the following:
<list list-type="order"><list-item>
      <p id="d1e1558">Higher RH<inline-formula><mml:math id="M100" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:math></inline-formula>- and <inline-formula><mml:math id="M101" display="inline"><mml:mrow><mml:msub><mml:mi>W</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>-volume fractions for gradually dissipating clouds (by rising cloud base) with an increase in aerosol concentration. This is manifested by a slower transition from red to blue colors in Fig. 5. It can be explained by the fact that more aerosols increase the convective intensity and extend the core size, while efficiently losing the margins, yielding a higher-core-volume fraction out of the total cloud.</p></list-item><list-item>
      <p id="d1e1582">The likelihood of finding dissipating cloud fragments with a <inline-formula><mml:math id="M102" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> increases with a decrease in aerosol concentration. For the polluted case most of the dissipating clouds lack a <inline-formula><mml:math id="M103" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>. This effect was seen in Fig. 1 and explained in Sect. 3.2, showing that downdrafts promote heating and positive buoyancy in low aerosol concentration cases where evaporation efficiency (and hence cooling) is limited. This effect is checked for the cloud field scale in Sect. 4.2.</p></list-item></list>
As opposed to the single cloud simulations (Sect. 3) where cloud lifetime
can be easily defined, in cloud field simulations (especially the cleaner
cases) many clouds do not live as individual clouds from formation to
dissipation but rather split and merge with other clouds continuously
(Heiblum et al., 2016b). Thus, in order to evaluate the
lifetime evolution of cores in cloud fields, we focus on the growing branch
and use cloud mass (kg) as a proxy for the cloud lifetime during its initial
and mature stages. We assume that in the vicinity of the growing branch a
larger mass corresponds to a later stage in its lifetime.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F7" specific-use="star"><?xmltex \currentcnt{7}?><label>Figure 7</label><caption><p id="d1e1610">CvM space diagrams showing the pixel fractions (<inline-formula><mml:math id="M104" display="inline"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mi mathvariant="normal">pixel</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) of
<inline-formula><mml:math id="M105" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> within RH<inline-formula><mml:math id="M106" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:math></inline-formula> <bold>(a, d, g)</bold>, B<inline-formula><mml:math id="M107" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:math></inline-formula> within <inline-formula><mml:math id="M108" display="inline"><mml:mrow><mml:msub><mml:mi>W</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> <bold>(b, e, h)</bold>,
and RH<inline-formula><mml:math id="M109" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:math></inline-formula> within <inline-formula><mml:math id="M110" display="inline"><mml:mrow><mml:msub><mml:mi>W</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> <bold>(c, f, i)</bold> for the clean (top row, <bold>a, b, c</bold>),
intermediate (middle row, <bold>d, e, f</bold>), and polluted (bottom row, <bold>g, h, i</bold>)
simulations. Bright colors indicate high-pixel fractions (large overlap
between two core types), while dark colors indicate low-pixel fractions
(little overlap between two core types). The differences in the scatter
density and location for different panels are due to the fact that only
clouds which contain a core fraction above zero (for the core in question)
are considered.</p></caption>
          <?xmltex \igopts{width=441.017717pt}?><graphic xlink:href="https://acp.copernicus.org/articles/19/10739/2019/acp-19-10739-2019-f07.png"/>

        </fig>

      <p id="d1e1710">In Fig. 6 the core mass and volume fractions (<inline-formula><mml:math id="M111" display="inline"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mi mathvariant="normal">mass</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M112" display="inline"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mi mathvariant="normal">vol</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, using
the RH definition) of all growing branch clouds are sorted by mass for the
three aerosol concentrations. We note that the higher cloud masses reached
by lower-aerosol-concentration simulation can be explained by cloud field
organization effects due to precipitation (i.e., increased merging of clouds)
rather than increased cloud condensation (Heiblum et al., 2016b; Seigel,
2014). The clean case starts off with the highest core fractions (both mass
and volume), which decrease steadily with an increase in mass (or increase in
lifetime). For all concentrations, most of the cloud mass is concentrated in
the core region. The polluted case shows a slight increase in core mass
fractions with increase in mass, while the other two cases show decreases in
core mass fractions.</p>
      <p id="d1e1736">The core volume fractions show lower values than the mass fractions. The
clean clouds are margin dominated for<?pagebreak page10748?> most masses, and the polluted clouds
are core dominated for all masses. The intermediate case is generally
confined to values between the other two cases. Figure 6 can be considered
comparable with the lower panels in Fig. 3g and h, but excluding the dissipating
part of those time series. The similar findings in both figures indicate the
robustness of the aerosol effects on core properties in clouds.</p>
      <p id="d1e1739">Following the analyses of Sect. 3.1, we next test how aerosol concentration
affects the subset properties of one core type within another for all clouds
in a field (Fig. 7). We focus only on the typically smaller-sized cores
(<inline-formula><mml:math id="M113" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, RH<inline-formula><mml:math id="M114" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:math></inline-formula>) within larger-sized cores. Out of the three
permutations, the RH<inline-formula><mml:math id="M115" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:math></inline-formula> inside <inline-formula><mml:math id="M116" display="inline"><mml:mrow><mml:msub><mml:mi>W</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> shows the lowest sensitivity
to aerosol. All three growing branches (for the different aerosol
concentrations) consistently show that the RH<inline-formula><mml:math id="M117" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:math></inline-formula> is a subset of
<inline-formula><mml:math id="M118" display="inline"><mml:mrow><mml:msub><mml:mi>W</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> (i.e., RH<inline-formula><mml:math id="M119" display="inline"><mml:mrow><mml:msub><mml:mi/><mml:mi mathvariant="normal">core</mml:mi></mml:msub><mml:mo>⊆</mml:mo><mml:msub><mml:mi>W</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>), while the dissipation
branches show much lower overlap fraction between the two cores.</p>
      <p id="d1e1820">For the dissipating clouds in general, the lower the mass and the higher the
COG, the smaller the overlap. The dissipating branches do include a scatter
of small cloud for which RH<inline-formula><mml:math id="M120" display="inline"><mml:mrow><mml:msub><mml:mi/><mml:mi mathvariant="normal">core</mml:mi></mml:msub><mml:mo>⊆</mml:mo><mml:msub><mml:mi>W</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, comprised of
small cloud segments which shed off the main core regions of larger clouds.
These findings slightly differ from those of the single cloud simulations
that show RH<inline-formula><mml:math id="M121" display="inline"><mml:mrow><mml:msub><mml:mi/><mml:mi mathvariant="normal">core</mml:mi></mml:msub><mml:mo>⊆</mml:mo><mml:msub><mml:mi>W</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> for their entire lifetimes,
while for cloud fields this property breaks down during dissipation. This
difference highlights the importance of cloud interactions (i.e., splitting and
merging) and cloud field air flow patterns (i.e., organized advection,
updrafts, and downdrafts) in determining the relationships between core
types, enabling supersaturation and downdrafts to coincide in small
dissipating clouds.</p>
      <p id="d1e1857">The other two permutations (i.e., <inline-formula><mml:math id="M122" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> inside RH<inline-formula><mml:math id="M123" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:math></inline-formula>, <inline-formula><mml:math id="M124" display="inline"><mml:mrow><mml:msub><mml:mi>W</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>)
show significant changes due to aerosol. For the polluted case, <inline-formula><mml:math id="M125" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub><mml:mo>⊆</mml:mo><mml:msub><mml:mi>W</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> for nearly all clouds, including clouds at initial
stages of dissipation. Similar results are seen for <inline-formula><mml:math id="M126" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> inside
RH<inline-formula><mml:math id="M127" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:math></inline-formula>, but with slightly lower pixel fractions. The polluted case thus
illustrates the case of buoyancy production due to convective updraft. For
the lower aerosol concentrations, two main aerosol effects are seen:
<list list-type="order"><list-item>
      <p id="d1e1932">The lower the concentration, the lower the chance that <inline-formula><mml:math id="M128" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is a proper subset of the other cores for large growing branch clouds.</p></list-item><list-item>
      <p id="d1e1947">The lower the concentration, the more prevalent the independent dissipating branch <inline-formula><mml:math id="M129" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> that has little to no overlap with the other cores.</p></list-item></list>
For the case of <inline-formula><mml:math id="M130" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> within RH<inline-formula><mml:math id="M131" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:math></inline-formula>, the lower concentrations show
an almost-binary scenario where either <inline-formula><mml:math id="M132" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub><mml:mo>⊆</mml:mo><mml:msub><mml:mi mathvariant="normal">RH</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> or
<inline-formula><mml:math id="M133" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub><mml:mo>∉</mml:mo><mml:msub><mml:mi mathvariant="normal">RH</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>. These results bear similarity to the
single cloud simulations, where a quick transition (in time) from
<inline-formula><mml:math id="M134" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub><mml:mo>⊆</mml:mo><mml:msub><mml:mi mathvariant="normal">RH</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> to <inline-formula><mml:math id="M135" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub><mml:mo>∉</mml:mo><mml:msub><mml:mi mathvariant="normal">RH</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> was
seen. These results imply the existence of two different buoyancy production
processes (more in Sect. 4.2), one associated with supersaturation and the
other with subsaturation. In contrary, pixels fractions of <inline-formula><mml:math id="M136" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> inside
<inline-formula><mml:math id="M137" display="inline"><mml:mrow><mml:msub><mml:mi>W</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> span the entire range of values (i.e., partial overlaps between the
core types), as seen for both single clouds and cloud fields during
dissipation. This is to be expected due to a more direct physical link and
feedbacks between the <inline-formula><mml:math id="M138" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M139" display="inline"><mml:mrow><mml:msub><mml:mi>W</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F8" specific-use="star"><?xmltex \currentcnt{8}?><label>Figure 8</label><caption><p id="d1e2101">Analyses of dominant buoyancy term within <inline-formula><mml:math id="M140" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> of clouds
(see text for details). As seen in previous figures, rows represent clean
(top, <bold>a, b, c</bold>), intermediate (middle, <bold>d, e, f</bold>), and polluted (bottom, <bold>g, h, i</bold>)
simulations. Columns represent dependence on maximum absolute vertical
velocity within cloud <bold>(a, d, g)</bold>, dependence on partition of total cloud mass
to cloud droplets and rain drops <bold>(b, e, h)</bold>, and CvM space diagrams of all
clouds with <inline-formula><mml:math id="M141" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, where red (blue) shades indicate temperature
(humidity) buoyancy terms that dominate the cloud <bold>(c, f, i)</bold>. Legends include
percentage of clouds that are <inline-formula><mml:math id="M142" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> or <inline-formula><mml:math id="M143" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">Qv</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> dominated (see text for
explanation).</p></caption>
          <?xmltex \igopts{width=441.017717pt}?><graphic xlink:href="https://acp.copernicus.org/articles/19/10739/2019/acp-19-10739-2019-f08.png"/>

        </fig>

</sec>
<?pagebreak page10749?><sec id="Ch1.S4.SS2">
  <label>4.2</label><title>Analysis of cloud field buoyancy</title>
      <p id="d1e2181">In Sect. 3.2 it was seen that for single clouds, positive buoyancy results
from two main mechanisms: (i) convective updrafts – where updrafts promote
supersaturation and latent heat release, and thus always positive <inline-formula><mml:math id="M144" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">Qv</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and frequently positive <inline-formula><mml:math id="M145" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> – and (ii) dissipative downdrafts – where
subsaturated cloudy downdrafts promote a positive <inline-formula><mml:math id="M146" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and neutral
<inline-formula><mml:math id="M147" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">Qv</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>. The latter case is dependent on low evaporation efficiency and
hence seen mostly for precipitating stages of low aerosol concentration
simulations. In Fig. 8 we perform a similar test for the cloud field scale.
Instead of analyzing pixel by pixel, we check whether each buoyancy core
within a cloud is <inline-formula><mml:math id="M148" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> or <inline-formula><mml:math id="M149" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">Qv</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> dominated. To quantify this we use a
normalized buoyancy dominance parameter <inline-formula><mml:math id="M150" display="inline"><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mrow><mml:mi mathvariant="normal">Σ</mml:mi><mml:msub><mml:mi mathvariant="normal">pixel</mml:mi><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:msub><mml:mo>-</mml:mo><mml:mi mathvariant="normal">Σ</mml:mi><mml:msub><mml:mi mathvariant="normal">pixel</mml:mi><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">Qv</mml:mi></mml:msub><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mi mathvariant="normal">Σ</mml:mi><mml:msub><mml:mi mathvariant="normal">pixel</mml:mi><mml:mrow><mml:mi>B</mml:mi><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:mstyle></mml:math></inline-formula>, where a
core comprised of only <inline-formula><mml:math id="M151" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:math></inline-formula> (<inline-formula><mml:math id="M152" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">Qv</mml:mi></mml:msub><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:math></inline-formula>)
pixels yields 1 (<inline-formula><mml:math id="M153" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula>). Hence, we expect negative (positive) values to
indicate dominance of updraft buoyancy (downdrafts buoyancy).</p>
      <p id="d1e2344">Analysis of the buoyancy components in the CvM space (Fig. 8c, f, and i)
shows that the large majority of clouds are <inline-formula><mml:math id="M154" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">Qv</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> dominated. For all
concentrations, clouds initiate with all pixels showing <inline-formula><mml:math id="M155" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">Qv</mml:mi></mml:msub><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:math></inline-formula>. As clouds develop along the growing branch the
<inline-formula><mml:math id="M156" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> becomes more abundant with <inline-formula><mml:math id="M157" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:math></inline-formula> pixels. This
is expected with increasing release of latent heat during cloud growth.
During dissipation <inline-formula><mml:math id="M158" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">Qv</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> again becomes the dominant component for the
majority of clouds. The polluted simulation shows an extreme case where all
buoyancy cores in the simulation are <inline-formula><mml:math id="M159" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">Qv</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> dominated, while for the
lower concentrations a portion of the dissipating and precipitating clouds
are <inline-formula><mml:math id="M160" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> dominated.</p>
      <p id="d1e2433">Thus, we hypothesize that the polluted simulation only permits buoyancy
cores of the updraft type which intersect with the other core types (i.e., <inline-formula><mml:math id="M161" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub><mml:mo>∈</mml:mo><mml:msub><mml:mi mathvariant="normal">RH</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M162" display="inline"><mml:mrow><mml:msub><mml:mi>W</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>), while the lower concentrations
also permit buoyancy cores of the downdraft type which do not intersect with
the other core types (i.e., <inline-formula><mml:math id="M163" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub><mml:mo>∉</mml:mo><mml:msub><mml:mi mathvariant="normal">RH</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M164" display="inline"><mml:mrow><mml:msub><mml:mi>W</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>). We
test this by observing the relation of cloud maximum absolute vertical
velocity (Fig. 8a, d, and g) and mean drop size (Fig. 8b, e, and h)
with the relative dominance of the buoyancy terms. Absolute vertical
velocity is chosen to represent both updrafts and downdrafts. The data are
further separated into independent (<inline-formula><mml:math id="M165" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub><mml:mo>∉</mml:mo><mml:msub><mml:mi mathvariant="normal">RH</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>,
<inline-formula><mml:math id="M166" display="inline"><mml:mrow><mml:msub><mml:mi>W</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) and dependent (<inline-formula><mml:math id="M167" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub><mml:mo>∈</mml:mo><mml:msub><mml:mi mathvariant="normal">RH</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M168" display="inline"><mml:mrow><mml:msub><mml:mi>W</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) buoyancy
subsets of the data by that separating to buoyant cores within updrafts and
downdrafts. Clear aerosol effects are seen on cloud mean drop size and
maximal <inline-formula><mml:math id="M169" display="inline"><mml:mrow><mml:mo>|</mml:mo><mml:mi>W</mml:mi><mml:mo>|</mml:mo></mml:mrow></mml:math></inline-formula>. As expected, there is a decrease in drop size
with increase in aerosol concentration and increase in maximal velocity.
Regarding cloud field buoyancy, as predicted, the independent buoyancy cores
are more frequently <inline-formula><mml:math id="M170" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> dominated than the dependent buoyancy cores.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F9" specific-use="star"><?xmltex \currentcnt{9}?><label>Figure 9</label><caption><p id="d1e2579"><bold>(a, g, g)</bold> Relative humidity (RH; %) vertical
cross-sections slicing through the center of gravity of the most massive
cloud in each simulation. <bold>(b, e, h)</bold> and <bold>(c, f, i)</bold> display CvM space
diagrams of mean cloud margin RH and mean cloud core RH,
respectively, using the RH<inline-formula><mml:math id="M171" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:math></inline-formula> definition. The upper <bold>(a, b, c)</bold>, middle <bold>(d, e, f)</bold>, and lower <bold>(g, h, i)</bold> panels correspond to the clean, intermediate, and
polluted aerosol cases. Notice that the different color bar ranges for margin and
core mean RH panels.</p></caption>
          <?xmltex \igopts{width=441.017717pt}?><graphic xlink:href="https://acp.copernicus.org/articles/19/10739/2019/acp-19-10739-2019-f09.png"/>

        </fig>

      <p id="d1e2615">The polluted case is populated with dependent cores (white scatter) and
shows a classic pre-precipitation convective growth scenario, where relative
dominance of the <inline-formula><mml:math id="M172" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> term increases linearly with increase in cloud mean
drop size. A logarithmic dependence of <inline-formula><mml:math id="M173" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> dominance on maximal <inline-formula><mml:math id="M174" display="inline"><mml:mrow><mml:mo>|</mml:mo><mml:mi>W</mml:mi><mml:mo>|</mml:mo></mml:mrow></mml:math></inline-formula> is seen, which saturates at high maximal <inline-formula><mml:math id="M175" display="inline"><mml:mrow><mml:mo>|</mml:mo><mml:mi>W</mml:mi><mml:mo>|</mml:mo></mml:mrow></mml:math></inline-formula>. This
can be explained by the fact that increased convection mainly increases the
abundance of pixels with <inline-formula><mml:math id="M176" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:math></inline-formula>, but without changing the
fact that the entire cloud is <inline-formula><mml:math id="M177" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">Qv</mml:mi></mml:msub><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:math></inline-formula>, so that <inline-formula><mml:math id="M178" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is
unlikely to become the dominant term. The lower concentrations show a more
complex scenario. These simulations show a superposition of dependent core
convective growth behavior (i.e., the scatter pattern seen for the polluted
case) and additional populations of both dependent (other white scatter
points) and independent (black scatter) cores.</p>
      <p id="d1e2706">The independent cores span all the range of possibilities of <inline-formula><mml:math id="M179" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and
<inline-formula><mml:math id="M180" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">Qv</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> relative dominance. They tend to have larger cloud mean drop
sizes, and a near-zero maximum <inline-formula><mml:math id="M181" display="inline"><mml:mrow><mml:mo>|</mml:mo><mml:mi>W</mml:mi><mml:mo>|</mml:mo></mml:mrow></mml:math></inline-formula>, indicating that they only
form at late non-convective stages of cloud development. Furthermore, a
trend is seen for the subset of scatter that is <inline-formula><mml:math id="M182" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> dominated, where a
positive (negative) correlation between mean drop size (maximal <inline-formula><mml:math id="M183" display="inline"><mml:mrow><mml:mo>|</mml:mo><mml:mi>W</mml:mi><mml:mo>|</mml:mo></mml:mrow></mml:math></inline-formula>) and <inline-formula><mml:math id="M184" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> dominance is seen. This again stresses the
importance of drop size on the formation of positive buoyancy within
downdrafts and highlights the fact that <inline-formula><mml:math id="M185" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> should be largest (and most
abundant) below the downdraft equilibrium level, when the <inline-formula><mml:math id="M186" display="inline"><mml:mrow><mml:mo>|</mml:mo><mml:mi>W</mml:mi><mml:mo>|</mml:mo></mml:mrow></mml:math></inline-formula>
approaches zero. The independent cores that are <inline-formula><mml:math id="M187" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> dominated thus
fulfill the characteristics of the downdraft buoyancy production process, while
the independent cores that are <inline-formula><mml:math id="M188" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">Qv</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> dominated may originate from larger
clouds (shedding mechanism) with high humidity content, have weak <inline-formula><mml:math id="M189" display="inline"><mml:mrow><mml:mo>|</mml:mo><mml:mi>W</mml:mi><mml:mo>|</mml:mo></mml:mrow></mml:math></inline-formula>, and are slow to evaporate.</p>
      <p id="d1e2835">The intermediate simulation shows an additional scatter area of dependent
core clouds with increasing <inline-formula><mml:math id="M190" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> relative dominance for lower maximal
<inline-formula><mml:math id="M191" display="inline"><mml:mrow><mml:mo>|</mml:mo><mml:mi>W</mml:mi><mml:mo>|</mml:mo></mml:mrow></mml:math></inline-formula>, located between the independent core clouds and the
convective growth core clouds. These clouds may represent a gradual
transition from <inline-formula><mml:math id="M192" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">Qv</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> dominance to <inline-formula><mml:math id="M193" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> dominance during dissipation
which is only possible in the intermediate simulation. This scatter area is
absent from the clean and polluted simulation, in the former case due to
absence of the gradual dissipation pathway and in the latter case due to
efficient evaporation eliminating <inline-formula><mml:math id="M194" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> during dissipation. We note that
the intermediate case shows a slightly higher percentage of clouds that are
<inline-formula><mml:math id="M195" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> dominated (see legends in Fig. 8) than the clean case. This can be
due to stronger convection in this simulation (i.e., increased <inline-formula><mml:math id="M196" display="inline"><mml:mrow><mml:mo>|</mml:mo><mml:mi>W</mml:mi><mml:mo>|</mml:mo></mml:mrow></mml:math></inline-formula> range), which favors increased mixing with the dry environment
(see Fig. 9) and the formation of unsaturated strong downdrafts that descend
below the level of neutral buoyancy.</p>
</sec>
<?pagebreak page10751?><sec id="Ch1.S4.SS3">
  <label>4.3</label><title>Aerosol effects on cloud relative humidity</title>
      <p id="d1e2926">From Fig. 3 it was demonstrated that a large part of the differences in single
cloud characteristics (such as mass, volume, and the partition of these to
core and margin regions) due to aerosols can be attributed to differences in
vapor diffusion efficiencies. In Fig. 9 we check how these aerosol effects
are manifested in the cloud field scale (using the CvM space) by observing
the mean RH in the cloud core and margin of all clouds,
where the core (margin) mean RH can be taken as a proxy for condensation
(evaporation) efficiency. To gain additional intuition regarding the
distribution of RH values within the clouds, vertical cross-sections
(parallel to the prevailing wind direction) of the most massive clouds from
each simulation are shown.</p>
      <p id="d1e2929">The vertical cross-sections demonstrate the large differences in the massive
clouds for each of the simulations. In addition to the increase in
precipitation production, lower aerosol concentrations yield much larger
horizontal extents of clouds. The clean, intermediate, and polluted most
massive clouds have a maximum radius of <inline-formula><mml:math id="M197" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M198" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula>, and <inline-formula><mml:math id="M199" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 0.5 km, respectively. It is clear from the
cross-section that the clean cloud is actually composed of two large clouds
which merge together. For the clean case, the highest RH values are reached
slightly below the cloud top. The edges of the clouds show subsaturation
conditions, with the lowest RH values observed below the lifting condensation level (LCL; precipitation
regions) and at the upper interface of the cloud with the environments.</p>
      <p id="d1e2959">The intermediate-case cloud shows lower maximal and minimal RH values and an
increased dominance of the margin region. This cloud penetrates the
inversion layer and entrains dry air into the cloud. In addition, the cloud
produces significant precipitation which initiates downdrafts of dry
entrained air through the cloud center. It can be seen that the increased
vertical development of the intermediate-case cloud in comparison with the
clean case increases the mixing with the environment. Thus, the dynamic
effect of increased mixing and reduction in cloud RH overcomes the
microphysical effect of increased evaporation and increase in cloud RH. The
polluted-case cloud, on the other hand, shows a homogeneous RH pattern, with
most of the cloud showing around 100 % RH and only a thin layer at the
cloud edges (mainly at the upper regions) showing lower RH values. The
polluted cloud penetrates the inversion layer as well, but this case lacks
precipitation, and the microphysical effect of evaporation overcomes the
dynamical effect of mixing.</p>
      <p id="d1e2962">Keeping in mind the insights obtained from comparisons of individual cloud,
we move on to compare the RH characteristics of all clouds within the field.
Looking first at core mean RH, a robust decrease is seen with increase in
aerosol concentration. This decrease is seen for all cloud types and
locations within the CvM space. The polluted case displays the most
homogeneous pattern, with all clouds showing core mean RH values around
100 %, indicating efficient consumption of the supersaturation. The
intermediate case displays a slightly less homogeneous pattern, with values
ranging from 100 % to 101 % and with the higher values occurring along the
growing cloud branch, especially for the largest clouds. The clean case
shows the largest variance in core mean RH, ranging from 100 % for some
cloud fragments that soon start to dissipate to 103 % in the cores of the
large cloud entities. In addition to the low efficiency in consuming
supersaturation, the high RH values in clean large clouds are due to the
“protection” by large margin regions surrounding the core region.</p>
      <p id="d1e2966">The CvM patterns of mean margin RH show significant differences between the
polluted case and the other two. The mean margin RH values of the polluted
case are only marginally lower than 100 %, since subsaturated conditions
within the cloud are quickly adjusted by efficient evaporation. Only the
largest clouds in the polluted case permit lower mean margin RH values
(<inline-formula><mml:math id="M200" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">95</mml:mn></mml:mrow></mml:math></inline-formula> %) due to the entrainment of very dry environmental
pixels near the cloud tops (as seen in the vertical cross-section as well).
The intermediate and clean cases show similar patterns. The smaller mass
clouds (both growing and dissipating) show values above 95 %, while the
larger mass clouds show values as low as 85 %. The larger clouds are most
likely to reach low-RH areas near the inversion base and below the LCL (i.e., sub-cloudy layer) and entrain dry air and by that reduce the cloud margin
RH.</p>
      <p id="d1e2979">As seen in the vertical cross-section examples, the largest clouds in the
intermediate case have even lower margin RH values than for the clean case.
This can be explained by the increased development of the large intermediate
clouds to heights with lower RH and by more intense downdrafts for these
large clouds. The lowest RH values in the domain are seen for the
precipitating fragments (i.e., located below the adiabat). These fragments
typically contain low concentrations of large drop sizes (precipitation
drops) which are slow to evaporate and capable of surviving in low-RH
conditions within the sub-cloudy layer.</p>
</sec>
</sec>
<sec id="Ch1.S5" sec-type="conclusions">
  <label>5</label><title>Summary</title>
      <p id="d1e2992">In this work we explored how the aerosol effects on warm convective clouds
are reflected in their partition to core and margin regions. Following Part 1 of this work (PT1), we evaluated three types of core definitions: positive
buoyancy (<inline-formula><mml:math id="M201" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>), supersaturation (RH<inline-formula><mml:math id="M202" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:math></inline-formula>), and positive
vertical velocity (<inline-formula><mml:math id="M203" display="inline"><mml:mrow><mml:msub><mml:mi>W</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>). Both single cloud and cloud field models
have been used. For all aerosol concentrations (clean, intermediate, and
polluted), it is shown that the self-contained property of different core
types (i.e., <inline-formula><mml:math id="M204" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub><mml:mo>⊆</mml:mo><mml:msub><mml:mi mathvariant="normal">RH</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub><mml:mo>⊆</mml:mo><mml:msub><mml:mi>W</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) is
maintained for clouds during their growing and mature stages. This is
especially robust for the RH<inline-formula><mml:math id="M205" display="inline"><mml:mrow><mml:msub><mml:mi/><mml:mi mathvariant="normal">core</mml:mi></mml:msub><mml:mo>⊆</mml:mo><mml:msub><mml:mi>W</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> subset. The
<inline-formula><mml:math id="M206" display="inline"><mml:mrow><mml:msub><mml:mi>W</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and RH<inline-formula><mml:math id="M207" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:math></inline-formula> volume fractions decrease monotonically during
cloud growth, while <inline-formula><mml:math id="M208" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> initially increases and then decreases after
convection ceases. During growth, the RH<inline-formula><mml:math id="M209" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:math></inline-formula> (<inline-formula><mml:math id="M210" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) volume
fractions are largest for clean<?pagebreak page10752?> (polluted) clouds. This is due to low (high)
diffusion efficiencies, respectively, where efficient condensation promotes
<inline-formula><mml:math id="M211" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> at the expense of the RH<inline-formula><mml:math id="M212" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:math></inline-formula>.</p>
      <p id="d1e3141">During dissipation stages cores frequently cease to be subsets of one
another and may either increase or decrease in their volume fractions. In
cloud fields we also observe small cloud fragments which shed off larger
cloud entities. This shedding increases for the lower-concentration
simulations which produce long-lived large cloud entities due to cloud
merging. These fragments show large variance in volume fraction (for all
core types) magnitudes without any consistent behavior. This is due to the
fact that they shed off various locations of the cloud. The polluted,
non-precipitating cases are unique in that can one expect the <inline-formula><mml:math id="M213" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> to
decrease monotonically and remain the smallest and a proper subset of the
other cores.</p>
      <p id="d1e3155">For low aerosol concentrations, a <inline-formula><mml:math id="M214" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> may form during dissipation and
exist independently of the other core types. These cores are typically
located at the periphery of large clouds or throughout small precipitation
or dissipating cloud fragments. The increase in <inline-formula><mml:math id="M215" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> during dissipation
typically coincides with large drop sizes and precipitation production. The
fluctuations in <inline-formula><mml:math id="M216" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> for low concentrations may also create a
subsequent <inline-formula><mml:math id="M217" display="inline"><mml:mrow><mml:msub><mml:mi>W</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> but not of sufficient strength to also create a
RH<inline-formula><mml:math id="M218" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:math></inline-formula>. Hence, the RH<inline-formula><mml:math id="M219" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:math></inline-formula> can be considered the most
“well-behaved” and indicative of cloud lifetime, generally monotonically
decreasing in volume fraction irrespective of aerosol concentration.</p>
      <p id="d1e3221">We show that the <inline-formula><mml:math id="M220" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> in the warm convective cases considered here may
form by two main processes:
<list list-type="order"><list-item>
      <p id="d1e3237"><italic>Convective updrafts</italic>. Adiabatic cooling within updrafts promotes supersaturation, condensation, and release of latent heat. These cores are characterized by both positive temperature (<inline-formula><mml:math id="M221" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:math></inline-formula>) and humidity (<inline-formula><mml:math id="M222" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">Qv</mml:mi></mml:msub><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:math></inline-formula>) buoyancy terms.</p></list-item><list-item>
      <p id="d1e3273"><italic>Dissipative downdrafts</italic>. Subsaturated cloudy downdrafts follow a lapse rate which is unstable relative to the environmental one. These downdrafts undershoot the equilibrium level and become positively buoyant. These cores are characterized by positive temperature (<inline-formula><mml:math id="M223" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:math></inline-formula>) but neutral humidity (<inline-formula><mml:math id="M224" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">Qv</mml:mi></mml:msub><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:math></inline-formula>) buoyancy terms.</p></list-item></list>
The updraft buoyancy type is seen for all aerosol concentrations, while the
dissipation buoyancy type is only seen for lower aerosol concentrations. The
fact that the downdraft <inline-formula><mml:math id="M225" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is absent from polluted clouds highlights
the importance of drop size and its effect on evaporation rate. The high
(low) diffusion (collision coalescence) efficiencies in polluted clouds
maintain a small mean drop size and enable rapid evaporation during
entrainment, causing a negative effect on buoyancy. For lower
concentrations, clouds with a downdraft <inline-formula><mml:math id="M226" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">core</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> that only exist during late
mature, dissipation, and precipitating stages after drop size have grown
considerably. The larger mean drop sizes reduce evaporation rates, and the
cloudy downdrafts may thus descend nearly dry adiabatically and become
positively buoyant.</p>
      <p id="d1e3332">Focusing on cores using the RH definition, a cloud's mass (volume) is
dependent primarily on the processes in its core (margin). The core
increases cloud mass by condensation while the margin increases the cloud's
volume by mixing with the environment or dilution. The magnitude of the
effects in each region of the cloud is strongly dependent on the aerosol
concentration. Polluted clouds are core dominated both in terms of mass and
volume, since they can hardly maintain their margins. Clean clouds are also
core dominated in terms of mass but to a lesser degree. Clean clouds tend
to be margin dominated in terms of volume for most their lifetimes. Thus,
despite weaker convection in the clean clouds, their large, slow evaporating
margins enable their cores (and the entire cloud) to exist for longer time
spans by applying a large protecting shield around the core.</p>
      <p id="d1e3335">The different diffusion efficiencies are demonstrated by observing the
relative humidity (RH) values in clouds. Cleaner clouds show larger variance
in RH values. During their growing stages large supersaturation in the core
and subsaturation in the margin can be seen. During their dissipation
stages clouds may exist for minutes without any cloud core, with the entire
cloud at subsaturation. Polluted clouds show the opposite, with RH values
nearing 100 % throughout the cloud at all stages. Hence, above a certain
aerosol concentration, the saturation adjustment approximation (i.e., instant
condensation of all supersaturation) can be considered valid. However, the
transition from clean to polluted is not always linear. For example, the
largest clouds in the intermediate case have a lower margin RH value than both
the clean and polluted cases. This is due to the fact that the intermediate
case manages to develop taller (than the clean case) clouds with stronger
updrafts and downdrafts, which entrain drier air from above the inversion
layer base, but at the same time is less efficient in evaporating (than the
polluted case) water and adjusting the RH to 100 %.</p>
</sec>

      
      </body>
    <back><notes notes-type="dataavailability"><title>Data availability</title>

      <p id="d1e3342">The microphysical and thermodynamical profiles used to initialize the
single cloud and cloud field numerical simulations can be obtained upon
request from the corresponding author.</p>
  </notes><notes notes-type="authorcontribution"><title>Author contributions</title>

      <p id="d1e3348">RHH ran the cloud field simulations, conducted the analyses, and wrote
the final draft of paper. LP participated in writing the first draft and
performed single cloud simulations and relevant analyses. OA, GD, and IK
participated in paper editing and discussions.</p>
  </notes><notes notes-type="competinginterests"><title>Competing interests</title>

      <p id="d1e3354">The authors declare that they have no conflict of interest.</p>
  </notes><ack><title>Acknowledgements</title><p id="d1e3360">The authors would like to acknowledge the Weizmann Institute High
Performance Computing (HPC) team for their support.</p></ack><notes notes-type="financialsupport"><title>Financial support</title>

      <p id="d1e3365">The research leading to these results was supported by the Ministry of Science and Technology, Israel (grant no. 3-14444).</p>
  </notes><notes notes-type="reviewstatement"><title>Review statement</title>

      <p id="d1e3371">This paper was edited by Eric Jensen and reviewed by two anonymous referees.</p>
  </notes><ref-list>
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    <!--<article-title-html>Core and margin in warm convective clouds – Part 2: Aerosol effects on core properties</article-title-html>
<abstract-html><p>The effects of aerosol on warm convective cloud cores are evaluated using
single cloud and cloud field simulations. Three core definitions are
examined: positive vertical velocity (<i>W</i><sub>core</sub>), supersaturation
(RH<sub>core</sub>), and positive buoyancy (<i>B</i><sub>core</sub>). As presented in Part 1 (Heiblum et al., 2019),
the property <i>B</i><sub>core</sub> ⊆ RH<sub>core</sub> ⊆ <i>W</i><sub>core</sub> is
seen during growth of warm convective clouds. We show that this property is
kept irrespective of aerosol concentration. During dissipation core
fractions generally decrease with less overlap between cores. However, for
clouds that develop in low aerosol concentrations capable of producing
precipitation, <i>B</i><sub>core</sub> and subsequently <i>W</i><sub>core</sub> volume fractions may
increase during dissipation (i.e., loss of cloud mass). The RH<sub>core</sub>
volume fraction decreases during cloud lifetime and shows minor sensitivity
to aerosol concentration.</p><p>It is shown that a <i>B</i><sub>core</sub> forms due to two processes: (i) convective
updrafts – condensation within supersaturated updrafts and release of
latent heat – and (ii) dissipative downdrafts – subsaturated cloudy downdrafts
that warm during descent and <q>undershoot</q> the level of neutral buoyancy. The
former process occurs during cloud growth for all aerosol concentrations.
The latter process only occurs for low aerosol concentrations during
dissipation and precipitation stages where large mean drop sizes permit slow
evaporation rates and subsaturation during descent.</p><p>The aerosol effect on the diffusion efficiencies plays a crucial role in the
development of the cloud and its partition to core and margin. Using the
RH<sub>core</sub> definition, it is shown that the total cloud mass is mostly
dictated by core processes, while the total cloud volume is mostly dictated
by margin processes. Increase in aerosol concentration increases the core
(mass and volume) due to enhanced condensation but also decreases the margin
due to evaporation. In clean clouds larger droplets evaporate much slower,
enabling preservation of cloud size, and even increase by detrainment and
dilution (volume increases while losing mass). This explains how despite
having smaller cores and less mass, cleaner clouds may live longer and grow
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