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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-16-15413-2016</article-id><title-group><article-title>The source of discrepancies in aerosol–cloud–precipitation interactions between GCM and A-Train retrievals</article-title>
      </title-group><?xmltex \runningtitle{Aerosol--cloud--precipitation interactions in GCM and A-Train}?><?xmltex \runningauthor{T. Michibata et al.}?>
      <contrib-group>
        <contrib contrib-type="author" corresp="yes" rid="aff1 aff2">
          <name><surname>Michibata</surname><given-names>Takuro</given-names></name>
          <email>michibata@riam.kyushu-u.ac.jp</email>
        <ext-link>https://orcid.org/0000-0002-1491-0297</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff3">
          <name><surname>Suzuki</surname><given-names>Kentaroh</given-names></name>
          
        <ext-link>https://orcid.org/0000-0001-5315-2452</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff4">
          <name><surname>Sato</surname><given-names>Yousuke</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff2">
          <name><surname>Takemura</surname><given-names>Toshihiko</given-names></name>
          
        <ext-link>https://orcid.org/0000-0002-2859-6067</ext-link></contrib>
        <aff id="aff1"><label>1</label><institution>Department of Earth System Science and Technology, Kyushu University, Fukuoka, Japan</institution>
        </aff>
        <aff id="aff2"><label>2</label><institution>Research Institute for Applied Mechanics, Kyushu University, Fukuoka, Japan</institution>
        </aff>
        <aff id="aff3"><label>3</label><institution>Atmosphere and Ocean Research Institute, The University of Tokyo, Chiba, Japan</institution>
        </aff>
        <aff id="aff4"><label>4</label><institution>RIKEN Advanced Institute for Computational Science, Hyogo, Japan</institution>
        </aff>
      </contrib-group>
      <author-notes><corresp id="corr1">Takuro Michibata (michibata@riam.kyushu-u.ac.jp)</corresp></author-notes><pub-date><day>13</day><month>December</month><year>2016</year></pub-date>
      
      <volume>16</volume>
      <issue>23</issue>
      <fpage>15413</fpage><lpage>15424</lpage>
      <history>
        <date date-type="received"><day>17</day><month>September</month><year>2016</year></date>
           <date date-type="rev-request"><day>21</day><month>September</month><year>2016</year></date>
           <date date-type="rev-recd"><day>18</day><month>November</month><year>2016</year></date>
           <date date-type="accepted"><day>25</day><month>November</month><year>2016</year></date>
      </history>
      <permissions>
<license license-type="open-access">
<license-p>This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit <ext-link ext-link-type="uri" xlink:href="http://creativecommons.org/licenses/by/3.0/">http://creativecommons.org/licenses/by/3.0/</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>
    <p>Aerosol–cloud interactions are one of the most uncertain processes in
climate models due to their nonlinear complexity. A key complexity arises
from the possibility that clouds can respond to perturbed aerosols in two
opposite ways, as characterized by the traditional “cloud lifetime”
hypothesis and more recent “buffered system” hypothesis. Their importance
in climate simulations remains poorly understood. Here we investigate the
response of the liquid water path (LWP) to aerosol perturbations for warm
clouds from the perspective of general circulation model (GCM) and A-Train
remote sensing, through process-oriented model evaluations. A systematic
difference is found in the LWP response between the model results and
observations. The model results indicate a near-global uniform increase of
LWP with increasing aerosol loading, while the sign of the response of the
LWP from the A-Train varies from region to region. The satellite-observed
response of the LWP is closely related to meteorological and/or
macrophysical factors, in addition to the microphysics. The model does not reproduce this
variability of cloud susceptibility (i.e., sensitivity of LWP to perturbed
aerosols) because the parameterization of the autoconversion process assumes
only suppression of rain formation in response to increased cloud droplet
number, and does not consider macrophysical aspects that serve as a mechanism
for the negative responses of the LWP via enhancements of evaporation and
precipitation. Model biases are also found in the precipitation microphysics,
which suggests that the model generates rainwater readily even when little
cloud water is present. This essentially causes projections of
unrealistically frequent and light rain, with high cloud susceptibilities to
aerosol perturbations.</p>
  </abstract>
    </article-meta>
  </front>
<body>
      

<sec id="Ch1.S1" sec-type="intro">
  <title>Introduction</title>
      <p>Aerosol particles play an important indirect role in the climate system by
modifying cloud micro- and macrophysical properties, which is referred to as
aerosol–cloud interactions <xref ref-type="bibr" rid="bib1.bibx74 bib1.bibx4" id="paren.1"/>. An increase in
aerosols supplies more numerous cloud condensation nuclei, resulting in
numerous and smaller cloud droplets leading to brighter clouds, which is
known as the “albedo effect” <xref ref-type="bibr" rid="bib1.bibx74" id="paren.2"/>. Smaller cloud droplets
suppress the onset of precipitation in warm clouds due to the less efficient
collision–coalescence process, resulting in a longer cloud lifetime, which
is known as the “lifetime effect” <xref ref-type="bibr" rid="bib1.bibx4" id="paren.3"/>. There has been much
discussion about the climatic impacts of aerosol-induced modulation of water
clouds, which are particularly sensitive to aerosol perturbations
<xref ref-type="bibr" rid="bib1.bibx44 bib1.bibx7 bib1.bibx41 bib1.bibx33 bib1.bibx47 bib1.bibx71 bib1.bibx72" id="paren.4"><named-content content-type="pre">e.g.,</named-content></xref>.
However, quantitative estimates of radiative forcing with regard to
aerosol–cloud–precipitation–climate interactions remain uncertain, as
reported in the Fifth Assessment Report of the Intergovernmental Panel on
Climate Change (2013).</p>
      <p>One of the most important factors that quantify the magnitude of
aerosol–cloud interactions is the response of the cloud liquid water path
(LWP) to aerosol perturbations. This factor also characterizes aerosol
impacts on the global hydrological cycle through its representation of the
aerosol effect on precipitation efficiency. This effect is represented in
general circulation models (GCMs) as aerosol-induced changes in rainwater
production from cloud water, which are parameterized with a bulk microphysics
as the so-called autoconversion process. The water conversion rate by this
process (<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>P</mml:mi><mml:mtext>aut</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>) is generally given as a function of the liquid water
content (<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>L</mml:mi><mml:mtext>c</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>) and cloud droplet number concentration (<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mtext>c</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>) as
          <disp-formula id="Ch1.E1" content-type="numbered"><mml:math display="block"><mml:mrow><mml:msub><mml:mi>P</mml:mi><mml:mtext>aut</mml:mtext></mml:msub><mml:mo>∼</mml:mo><mml:msubsup><mml:mi>L</mml:mi><mml:mtext>c</mml:mtext><mml:mi mathvariant="italic">α</mml:mi></mml:msubsup><mml:mo>×</mml:mo><mml:msubsup><mml:mi>N</mml:mi><mml:mtext>c</mml:mtext><mml:mrow><mml:mo>-</mml:mo><mml:mi mathvariant="italic">β</mml:mi></mml:mrow></mml:msubsup><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
        where <inline-formula><mml:math display="inline"><mml:mi mathvariant="italic">α</mml:mi></mml:math></inline-formula> and <inline-formula><mml:math display="inline"><mml:mi mathvariant="italic">β</mml:mi></mml:math></inline-formula> are prescribed constants
<xref ref-type="bibr" rid="bib1.bibx6 bib1.bibx5 bib1.bibx25" id="paren.5"><named-content content-type="pre">e.g.,</named-content></xref>. The <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mtext>c</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> is then
somehow related to the aerosol number concentration (<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mtext>a</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>). In GCMs, Eq. (<xref ref-type="disp-formula" rid="Ch1.E1"/>) provides the only pathway through which aerosols
modulate precipitation formation and, thus, the cloud lifetime. Note that
GCMs also partly include the opposing processes (decreasing LWP due to
enhancement in evaporation) via the so-called direct and semi-direct effect
<xref ref-type="bibr" rid="bib1.bibx2 bib1.bibx23" id="paren.6"><named-content content-type="pre">e.g.,</named-content></xref>. Given that rainwater production is
always suppressed with increasing <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mtext>c</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> according to Eq. (<xref ref-type="disp-formula" rid="Ch1.E1"/>), GCMs tend to increase the LWP uniformly with increasing
<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mtext>c</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> for stratiform clouds.</p>
      <p>On the other hand, some observational studies have shown two pathways of LWP
responses to perturbed aerosols, i.e., both increasing and decreasing
tendencies of LWP with increasing aerosols
<xref ref-type="bibr" rid="bib1.bibx37 bib1.bibx33 bib1.bibx8" id="paren.7"/>; the mechanisms for these opposing
responses cannot be understood by a simple microphysical argument alone, but
are likely to relate to macrophysical and meteorological factors as well
<xref ref-type="bibr" rid="bib1.bibx3 bib1.bibx37 bib1.bibx62 bib1.bibx33 bib1.bibx53 bib1.bibx19 bib1.bibx8" id="paren.8"><named-content content-type="pre">e.g.,</named-content></xref>.
<xref ref-type="bibr" rid="bib1.bibx83" id="text.9"/> found that there are processes that modify the cloud
geometric thickness to aerosol perturbations in such a way that cancels the
aerosol indirect effect at sufficiently long timescales. Such a compensation
mechanism is currently considered one of the “buffering effects”
<xref ref-type="bibr" rid="bib1.bibx60" id="paren.10"/>, which generate the opposite result to the original
hypotheses of cloud albedo and lifetime effects, for the cloud system as a
whole <xref ref-type="bibr" rid="bib1.bibx48 bib1.bibx31 bib1.bibx50" id="paren.11"/>. Despite its critical
importance to accurate climate simulations, the operation of this mechanism
at the global scale remains poorly understood.</p>
      <p>To determine the mechanisms involved in the competition between the
“lifetime effect” and “buffering effect”, the complexity in aerosol
effects on clouds needs to be untangled at a fundamental process-level. For
this purpose, GCMs should be evaluated extensively against observations in
the context of their process representations, which are key to the
aerosol–cloud–precipitation interaction.</p>
      <p>In this study, we analyze results from both GCM and A-Train data, with a
particular focus on their discrepancies in the key indices of aerosol–cloud
interactions relating to fundamental processes. The factors examined are the
susceptibilities of cloud optical thickness (<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mtext>c</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>), droplet effective
radius (<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mtext>e</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>), and LWP to <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mtext>c</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>. To focus directly on the cloud physical
parameters, we use <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mtext>c</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> as an aerosol proxy rather than <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mtext>a</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>
<xref ref-type="bibr" rid="bib1.bibx27" id="paren.12"><named-content content-type="pre">e.g.</named-content></xref>. A satellite-based study by <xref ref-type="bibr" rid="bib1.bibx8" id="text.13"/> reported
that cloud susceptibilities show similar results whether aerosol index,
aerosol optical depth (AOD), or <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mtext>c</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> are applied as an aerosol proxy (see
their supplementary information). Given the fundamental relationship of
<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mtext>c</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math display="inline"><mml:mo>∝</mml:mo></mml:math></inline-formula> LWP <inline-formula><mml:math display="inline"><mml:mo>/</mml:mo></mml:math></inline-formula> <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mtext>e</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>, the susceptibilities are related as follows
<xref ref-type="bibr" rid="bib1.bibx17" id="paren.14"/>:
          <disp-formula id="Ch1.E2" content-type="numbered"><mml:math display="block"><mml:mrow><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mtext>d</mml:mtext><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi>ln⁡</mml:mi><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mtext>c</mml:mtext></mml:msub></mml:mrow><mml:mrow><mml:mtext>d</mml:mtext><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi>ln⁡</mml:mi><mml:msub><mml:mi>N</mml:mi><mml:mtext>c</mml:mtext></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>=</mml:mo><mml:mo>-</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mtext>d</mml:mtext><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi>ln⁡</mml:mi><mml:msub><mml:mi>r</mml:mi><mml:mtext>e</mml:mtext></mml:msub></mml:mrow><mml:mrow><mml:mtext>d</mml:mtext><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi>ln⁡</mml:mi><mml:msub><mml:mi>N</mml:mi><mml:mtext>c</mml:mtext></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>+</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mtext>d</mml:mtext><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi>ln⁡</mml:mi><mml:mi mathvariant="normal">LWP</mml:mi></mml:mrow><mml:mrow><mml:mtext>d</mml:mtext><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi>ln⁡</mml:mi><mml:msub><mml:mi>N</mml:mi><mml:mtext>c</mml:mtext></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
        where the first and second terms on the right side of Eq. (<xref ref-type="disp-formula" rid="Ch1.E2"/>)
represent the “albedo effect” and the “lifetime effect”, respectively.
Equation (<xref ref-type="disp-formula" rid="Ch1.E2"/>) has the advantage that it can quantify the
contributions from the two effects that determine the aerosol impact on cloud
radiative properties. As discussed here and also in recent studies
<xref ref-type="bibr" rid="bib1.bibx17 bib1.bibx13" id="paren.15"/>, the two terms in Eq. (<xref ref-type="disp-formula" rid="Ch1.E2"/>) are
related to representations of different processes. This approach makes it
easier to understand the mechanisms that determine the resultant magnitude of
aerosol indirect forcing in the context of relevant processes
<xref ref-type="bibr" rid="bib1.bibx51" id="paren.16"/>.</p>
      <p>The aim of the study is to clarify the fundamental source of uncertainty in
process representations of aerosol–cloud–precipitation interactions in GCMs
for stratiform and shallow cumulative warm clouds (excluding deep convective
thick clouds or ice clouds; see Sect. 2). Given that the aerosol–cloud
interaction processes are also influenced by both macrophysics (e.g.,
environmental conditions, dynamical regime, cloud type) and microphysics, we
also place an emphasis on the importance of macrophysics
<xref ref-type="bibr" rid="bib1.bibx55 bib1.bibx20 bib1.bibx86" id="paren.17"><named-content content-type="pre">e.g.,</named-content></xref>.</p>
</sec>
<sec id="Ch1.S2">
  <title>Data</title>
<sec id="Ch1.S2.SS1">
  <title>MIROC–SPRINTARS</title>
      <p>A global climate model, Model for Interdisciplinary Research On Climate
(MIROC) version 5.2 <xref ref-type="bibr" rid="bib1.bibx79" id="paren.18"/>, was used in this study. The
interactions of the main tropospheric aerosols (i.e., black carbon, organic
matter, soil dust, sea salt, sulfate, and the precursor gases of sulfate)
with cloud–precipitation microphysics and radiation–climate effects are
incorporated in the aerosol module, Spectral Radiation-Transport Model for
Aerosol Species (SPRINTARS; <xref ref-type="bibr" rid="bib1.bibx67 bib1.bibx68 bib1.bibx69" id="altparen.19"/>),
which is coupled with MIROC (MIROC–SPRINTARS).</p>
      <p>The cloud macro- and microphysics framework in MIROC–SPRINTARS is based on a
prognostic large-scale condensation scheme, which explicitly considers
subgrid-scale variability of clouds <xref ref-type="bibr" rid="bib1.bibx78" id="paren.20"/>. This probability distribution function (PDF)-based
prognostic cloud scheme couples with the ice microphysics scheme proposed by
<xref ref-type="bibr" rid="bib1.bibx80" id="text.21"/>. MIROC–SPRINTARS treats both cloud droplets and ice
crystals as a two-moment bulk microphysics scheme <xref ref-type="bibr" rid="bib1.bibx70" id="paren.22"/>. The
nucleation of cloud droplets is parameterized by the scheme of
<xref ref-type="bibr" rid="bib1.bibx1" id="text.23"/>, and the process of cloud-to-rain water conversion
is diagnosed based on the <xref ref-type="bibr" rid="bib1.bibx6" id="text.24"/> autoconversion scheme. Rainwater
is not a prognostic variable in the current version of MIROC–SPRINTARS.</p>
      <p>We extracted warm-phase low clouds (<inline-formula><mml:math display="inline"><mml:mo>&gt;</mml:mo></mml:math></inline-formula> 273.15 <inline-formula><mml:math display="inline"><mml:mi mathvariant="normal">K</mml:mi></mml:math></inline-formula> in whole cloud
layers) from every 6 h instantaneous output for 5 full years; as a
result, 1 595 753 warm cloud samples were obtained. The horizontal and
vertical resolutions were T42 (approximately 2.8<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> <inline-formula><mml:math display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 2.8<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>
in latitude and longitude) and 20 layers, respectively. A more detailed
description of the model and its settings are documented in
<xref ref-type="bibr" rid="bib1.bibx38" id="text.25"/>.</p>
</sec>
<sec id="Ch1.S2.SS2">
  <title>CloudSat and MODIS</title>
      <p>We used the synergistic satellite data sets of the CloudSat and MODIS, which
are both part of the A-Train constellation <xref ref-type="bibr" rid="bib1.bibx57 bib1.bibx58" id="paren.26"/>.
The data products, 2B-TAU <xref ref-type="bibr" rid="bib1.bibx45" id="paren.27"/>, 2B-GEOPROF
<xref ref-type="bibr" rid="bib1.bibx35" id="paren.28"/>, and ECMWF-AUX <xref ref-type="bibr" rid="bib1.bibx40" id="paren.29"/> were used for the
period June 2006 to April 2011, i.e., a total of 5 full years. This
facilitated the construction of stable statistics with a horizontal
resolution (2.5<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> grid boxes in this study) close to the GCM output. We
defined the cloud layer as where the cloud mask value is greater than 30 from the
2B-GEOPROF product, which means a good, or strong, echo with high-confidence
detection <xref ref-type="bibr" rid="bib1.bibx35" id="paren.30"/>. The analysis was restricted to single-layer
water clouds; in total, 7 872 426 cloud samples were obtained.</p>
      <p>The LWP was derived from the MODIS-retrieved optical thickness and effective
radius using the following equation for an adiabatically stratified cloud
<xref ref-type="bibr" rid="bib1.bibx66" id="paren.31"/>:
            <disp-formula id="Ch1.E3" content-type="numbered"><mml:math display="block"><mml:mrow><mml:mi mathvariant="normal">LWP</mml:mi><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mn mathvariant="normal">5</mml:mn><mml:mn mathvariant="normal">9</mml:mn></mml:mfrac></mml:mstyle><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mtext>c</mml:mtext></mml:msub><mml:msub><mml:mi mathvariant="normal">r</mml:mi><mml:mtext>e</mml:mtext></mml:msub><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula>
          <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mtext>c</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> was also calculated based on an adiabatic assumption <xref ref-type="bibr" rid="bib1.bibx82" id="paren.32"/>
as
            <disp-formula id="Ch1.E4" content-type="numbered"><mml:math display="block"><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mtext>c</mml:mtext></mml:msub><mml:mo>=</mml:mo><mml:msqrt><mml:mn mathvariant="normal">2</mml:mn></mml:msqrt><mml:msup><mml:mi>B</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msup><mml:msup><mml:msub><mml:mi mathvariant="normal">Γ</mml:mi><mml:mtext>eff</mml:mtext></mml:msub><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>/</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msup><mml:mi mathvariant="normal">LWP</mml:mi><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>/</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:mrow><mml:mrow><mml:msubsup><mml:mi>r</mml:mi><mml:mtext>e</mml:mtext><mml:mn mathvariant="normal">3</mml:mn></mml:msubsup></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
          where <inline-formula><mml:math display="inline"><mml:mi>B</mml:mi></mml:math></inline-formula> <inline-formula><mml:math display="inline"><mml:mrow><mml:mo>=</mml:mo><mml:mo>(</mml:mo><mml:mn mathvariant="normal">3</mml:mn><mml:mo>/</mml:mo><mml:mn mathvariant="normal">4</mml:mn><mml:mi mathvariant="italic">π</mml:mi><mml:msub><mml:mi mathvariant="italic">ρ</mml:mi><mml:mtext>w</mml:mtext></mml:msub><mml:msup><mml:mo>)</mml:mo><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>/</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup><mml:mo>=</mml:mo></mml:mrow></mml:math></inline-formula> 0.0620 <inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="normal">kg</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>/</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula>,
<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ρ</mml:mi><mml:mtext>w</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> is the density of liquid water, and <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Γ</mml:mi><mml:mtext>eff</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> is the
adiabatic rate (<inline-formula><mml:math display="inline"><mml:mrow><mml:mi mathvariant="normal">g</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">km</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>) of increase in the liquid water
content with height (see also <xref ref-type="bibr" rid="bib1.bibx29" id="altparen.33"/> for more details of
derivation). We note that satellite data inherently include uncertainties
stemming from retrieval assumptions, which are not replicated in the model
output. Although it could be a part of the reason for discrepancies between the
model and observations, this would mostly be canceled when susceptibilities
of cloud and precipitation to aerosol loading are evaluated by a logarithmic
form. This study applies the uncertainty thresholds of <inline-formula><mml:math display="inline"><mml:mo>&lt;</mml:mo></mml:math></inline-formula> 5 and <inline-formula><mml:math display="inline"><mml:mo>&lt;</mml:mo></mml:math></inline-formula> 1 <inline-formula><mml:math display="inline"><mml:mrow><mml:mi mathvariant="normal">µ</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula> for <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mtext>c</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mtext>e</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> from the 2B-TAU product,
respectively, which contributes to the reduction of the retrieval uncertainty of
<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mtext>c</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> described above as much as possible <xref ref-type="bibr" rid="bib1.bibx39" id="paren.34"/>.</p>
      <p>To examine the cloud-to-rain conversion process, the conversion rate
(<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>P</mml:mi><mml:mtext>conv</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>) contributed by both autoconversion (collision–coalescence of
cloud droplets) and accretion (collision of cloud droplets by raindrops) was
derived from the approximation suggested by <xref ref-type="bibr" rid="bib1.bibx56" id="text.35"/>. This method
is established by the continuous collection equation <xref ref-type="bibr" rid="bib1.bibx46" id="paren.36"/>
using observed drop size distributions. <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>P</mml:mi><mml:mtext>conv</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> was estimated from MODIS
LWP and CloudSat mean cloud-layer radar reflectivity <inline-formula><mml:math display="inline"><mml:mover accent="true"><mml:mi>Z</mml:mi><mml:mo mathvariant="normal">‾</mml:mo></mml:mover></mml:math></inline-formula> as
            <disp-formula id="Ch1.E5" content-type="numbered"><mml:math display="block"><mml:mrow><mml:msub><mml:mi>P</mml:mi><mml:mtext>conv</mml:mtext></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>c</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mtext>LWP</mml:mtext><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mover accent="true"><mml:mi>Z</mml:mi><mml:mo mathvariant="normal">‾</mml:mo></mml:mover><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi>H</mml:mi><mml:mo>[</mml:mo><mml:mi>Z</mml:mi><mml:mo>-</mml:mo><mml:msub><mml:mi>Z</mml:mi><mml:mtext>c</mml:mtext></mml:msub><mml:mo>]</mml:mo><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
          where <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>c</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mo>/</mml:mo><mml:msup><mml:mn mathvariant="normal">2</mml:mn><mml:mn mathvariant="normal">6</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> is a coefficient from the collection kernel
<xref ref-type="bibr" rid="bib1.bibx34" id="paren.37"/> with <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mo>=</mml:mo><mml:mn>1.9</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mn>10</mml:mn><mml:mn>11</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> cm<inline-formula><mml:math 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> s<inline-formula><mml:math 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> and sixth moment factor with radar reflectivity. <inline-formula><mml:math display="inline"><mml:mrow><mml:mi>H</mml:mi><mml:mo>[</mml:mo><mml:mi>Z</mml:mi><mml:mo>-</mml:mo><mml:msub><mml:mi>Z</mml:mi><mml:mtext>c</mml:mtext></mml:msub><mml:mo>]</mml:mo></mml:mrow></mml:math></inline-formula> is
the Heaviside step function to exclude the cases that are less than the critical
radar threshold <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>Z</mml:mi><mml:mtext>c</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> of <inline-formula><mml:math display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>15 <inline-formula><mml:math display="inline"><mml:mrow><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msub><mml:mi mathvariant="normal">dBZ</mml:mi><mml:mi>e</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> for which the conversion
process is negligible <xref ref-type="bibr" rid="bib1.bibx36" id="paren.38"/>. Although this formulation is
based on marine stratocumulus cases from DYCOMS-II measurements
<xref ref-type="bibr" rid="bib1.bibx75" id="paren.39"/>, it is applicable for global analysis to study
aerosol–cloud interactions <xref ref-type="bibr" rid="bib1.bibx56 bib1.bibx55" id="paren.40"/> in drizzling
light-rain cases (<inline-formula><mml:math display="inline"><mml:mrow><mml:mover accent="true"><mml:mi>Z</mml:mi><mml:mo mathvariant="normal">‾</mml:mo></mml:mover><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mo>&lt;</mml:mo><mml:mn> 0</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msub><mml:mi mathvariant="normal">dBZ</mml:mi><mml:mi>e</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>). The
parameterization and assumptions used in this method (Eq. <xref ref-type="disp-formula" rid="Ch1.E5"/>)
are also valid for comparison between observations and model simulation
<xref ref-type="bibr" rid="bib1.bibx61" id="paren.41"/>. This brings valuable understanding for microphysical
conversion processes and its timescales, which matches the scope of our
study.</p>
      <p>Lower-tropospheric stability (LTS) was derived from the ECMWF-AUX product as the
difference in potential temperatures between 700 hPa and the surface
<xref ref-type="bibr" rid="bib1.bibx26" id="paren.42"/>, and is used for a metric of macroscopic thermodynamic
conditions.</p>
</sec>
</sec>
<sec id="Ch1.S3">
  <title>Results</title>
<sec id="Ch1.S3.SS1">
  <title>Precipitation microphysics</title>
      <p>A commonly known problem in GCMs associated with low cloud precipitation
microphysics is the timing of precipitation and its frequency and/or intensity
<xref ref-type="bibr" rid="bib1.bibx64 bib1.bibx65" id="paren.43"/>. This issue is also related to the magnitudes
of the aerosol indirect effect, i.e., dependency of precipitation on <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mtext>c</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>.
As a proxy for this, we use the precipitation susceptibility (<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mtext>p</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>)
metric, defined as
            <disp-formula id="Ch1.E6" content-type="numbered"><mml:math display="block"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mtext>p</mml:mtext></mml:msub><mml:mo>=</mml:mo><mml:mo>-</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mtext>d</mml:mtext><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi>ln⁡</mml:mi><mml:mi>R</mml:mi></mml:mrow><mml:mrow><mml:mtext>d</mml:mtext><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi>ln⁡</mml:mi><mml:msub><mml:mi>N</mml:mi><mml:mtext>c</mml:mtext></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
          where <inline-formula><mml:math display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula> is the rain rate. Observed values of <inline-formula><mml:math display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula> are derived from CloudSat
radar reflectivity through the <inline-formula><mml:math display="inline"><mml:mrow><mml:mi>Z</mml:mi><mml:mo>-</mml:mo><mml:mi>R</mml:mi></mml:mrow></mml:math></inline-formula> relationship <xref ref-type="bibr" rid="bib1.bibx9" id="paren.44"/>,
while model values of <inline-formula><mml:math display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula> are obtained as the large-scale precipitation rate.
We apply a threshold of <inline-formula><mml:math display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula> <inline-formula><mml:math display="inline"><mml:mo>&gt;</mml:mo></mml:math></inline-formula> 0.14 mm day<inline-formula><mml:math 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>, which is
equivalent to a radar reflectivity of <inline-formula><mml:math display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>15 <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">dBZ</mml:mi><mml:mi>e</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>
<xref ref-type="bibr" rid="bib1.bibx72" id="paren.45"/>, for precipitation in the model to enable a fair comparison
with satellite observations. The <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mtext>p</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> metric is useful for examining the
aerosol impact on precipitation <xref ref-type="bibr" rid="bib1.bibx54 bib1.bibx12" id="paren.46"/>.</p>
      <p>Figure <xref ref-type="fig" rid="Ch1.F1"/>a shows the behavior of <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mtext>p</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> as a function of the LWP
obtained from MIROC and A-Train satellite observations. The satellite <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mtext>p</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>
increases with increasing LWP up to around LWP <inline-formula><mml:math display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 450 g m<inline-formula><mml:math 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>; further increases in LWP result in a decrease in
<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mtext>p</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>. This behavior can be interpreted as follows <xref ref-type="bibr" rid="bib1.bibx54" id="paren.47"/>.
<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mtext>p</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> is low for a low LWP because clouds cannot generate much rainwater,
regardless of the aerosol loading. At a high LWP, <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mtext>p</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> is also low because
precipitation is dominant, regardless of the aerosol loading, due to the
abundant LWP. In other words, the LWP value at which the <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mtext>p</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> peaks
corresponds to the turning point where the water conversion process shifts
from the autoconversion regime to the accretion regime, as suggested by
previous studies <xref ref-type="bibr" rid="bib1.bibx85 bib1.bibx54" id="paren.48"/>.</p>
      <p>On the other hand, the <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mtext>p</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> amplitude predicted by MIROC is smaller than
the satellite results for a wide range of LWPs, and <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mtext>p</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> remains high even
after its values peak near LWP <inline-formula><mml:math display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 450 g m<inline-formula><mml:math 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>. This is
mainly because the autoconversion parameterization assumes a constant
dependency on <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mtext>c</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> (i.e., <inline-formula><mml:math display="inline"><mml:mi mathvariant="italic">β</mml:mi></mml:math></inline-formula>) regardless of the LWP, as is clear from
Eq. (<xref ref-type="disp-formula" rid="Ch1.E1"/>). This also leads to a significant overestimation of
<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mtext>p</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> for LWP <inline-formula><mml:math display="inline"><mml:mo>&lt;</mml:mo></mml:math></inline-formula> 100 g m<inline-formula><mml:math 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 means that the model
readily generates rainwater even when only a small amount of cloud water is
present.</p>
      <p>To understand the uncertainty in the conversion process from cloud water to
rainwater in more detail, we define a new metric, the “susceptibility of
microphysical conversion (<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mtext>conv</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>)” as
            <disp-formula id="Ch1.E7" content-type="numbered"><mml:math display="block"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mtext>conv</mml:mtext></mml:msub><mml:mo>=</mml:mo><mml:mo>-</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mtext>d</mml:mtext><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi>ln⁡</mml:mi><mml:msub><mml:mi>P</mml:mi><mml:mtext>conv</mml:mtext></mml:msub></mml:mrow><mml:mrow><mml:mtext>d</mml:mtext><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi>ln⁡</mml:mi><mml:msub><mml:mi>N</mml:mi><mml:mtext>c</mml:mtext></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula>
          This metric represents how aerosol burdens suppress rainwater production. In
satellite analysis, <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>P</mml:mi><mml:mtext>conv</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> can be estimated from the method proposed by
<xref ref-type="bibr" rid="bib1.bibx56" id="text.49"/>, as shown in Eq. (<xref ref-type="disp-formula" rid="Ch1.E5"/>). In the model,
<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>P</mml:mi><mml:mtext>conv</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> is obtained as a native output of the process rate. The method of
<xref ref-type="bibr" rid="bib1.bibx56" id="text.50"/> was compared with a native model output of the process
rate in a global cloud-resolving model (CRM) by <xref ref-type="bibr" rid="bib1.bibx61" id="text.51"/>. The study
showed that the radar reflectivity is a gross measure of the water conversion
timescale, supporting the underlying assumption of <xref ref-type="bibr" rid="bib1.bibx56" id="text.52"/>.
This implies that the <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mtext>conv</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>, which represents the timescale dependency
on <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mtext>c</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>, can be compared between satellite observations and model
simulations although absolute values of <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>P</mml:mi><mml:mtext>conv</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> can be different between
them. Although the use of satellite simulators would be helpful for more
direct comparison between model and observations, it is left as the subject
of future work.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F1"><caption><p>Susceptibilities of <bold>(a)</bold> precipitation <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mtext>p</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> and <bold>(b)</bold> microphysical
conversion <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mtext>conv</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> as a function of the liquid water path (LWP) for the
MIROC–SPRINTARS results and A-Train observations. The left axis shows the
value of the susceptibility (refer to the line graph), and the right (red) axis
shows the probability distribution function for each LWP bin (refer to the
bar chart).</p></caption>
          <?xmltex \igopts{width=227.622047pt}?><graphic xlink:href="https://acp.copernicus.org/articles/16/15413/2016/acp-16-15413-2016-f01.pdf"/>

        </fig>

      <p>As shown in Fig. <xref ref-type="fig" rid="Ch1.F1"/>b, MIROC overestimates <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mtext>conv</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>,
particularly in the lower LWP range. This means that the model generates
precipitation at a higher frequency, even at low LWPs, compared to
observations, which is mainly because the autoconversion in the model is too
rapid <xref ref-type="bibr" rid="bib1.bibx38 bib1.bibx65" id="paren.53"/>, as described above. Consequently, the
PDF of the LWP is biased toward lower
values because cloud water is depleted quickly by the rapid surface
precipitation. Alternatively, it is also possible that the model has biases
in the condensation processes, which lead to lower LWP and, thus, result in a
lower autoconversion rate. These tendencies in the model are strongly related
to unrealistically light rain that is too frequent, which is a common problem
in GCMs <xref ref-type="bibr" rid="bib1.bibx59" id="paren.54"/>, including MIROC.</p>
      <p>Besides this, <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mtext>conv</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> can also be biased from the error of cloud geometric
thickness due to insufficient vertical resolution in GCMs. In addition to the
microphysical aspects mentioned above, biases in macrophysical structure are
also related to model performances, which will be discussed later (see Sect. 3.3).</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F2" specific-use="star"><caption><p>Global distribution of <inline-formula><mml:math display="inline"><mml:mrow><mml:mi>d</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi>ln⁡</mml:mi><mml:mi mathvariant="normal">LWP</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mo>/</mml:mo><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi>d</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi>ln⁡</mml:mi><mml:msub><mml:mi>N</mml:mi><mml:mtext>c</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> from
(<bold>a</bold>, <bold>c</bold>) MIROC–SPRINTARS and (<bold>b</bold>, <bold>d</bold>) A-Train satellite estimations for
non-precipitating and precipitating clouds, respectively. The threshold of
the large-scale precipitation rate of 0.14 mm day<inline-formula><mml:math 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> is used to
distinguish between non-precipitating or precipitating events (see text for
details).</p></caption>
          <?xmltex \igopts{width=426.791339pt}?><graphic xlink:href="https://acp.copernicus.org/articles/16/15413/2016/acp-16-15413-2016-f02.pdf"/>

        </fig>

</sec>
<sec id="Ch1.S3.SS2">
  <title>Cloud susceptibilities</title>
      <p>The response of cloud liquid water to aerosol perturbations determines the
cloud lifetime via the modification of cloud fraction <xref ref-type="bibr" rid="bib1.bibx4" id="paren.55"/>,
and is thus related to global hydrological cycles as well as radiation budget
<xref ref-type="bibr" rid="bib1.bibx73 bib1.bibx84" id="paren.56"><named-content content-type="pre">e.g.,</named-content></xref>. As such, it is of great importance
to global climate studies to understand why there are two competing
mechanisms reported in the literature regarding the pathways of LWP, which
cause the LWP to either increase or decrease in response to an increase in
aerosols.</p>
      <p>Figure <xref ref-type="fig" rid="Ch1.F2"/> shows the geographical distributions of
LWP susceptibility (i.e., the second term on the right side in Eq. <xref ref-type="disp-formula" rid="Ch1.E2"/>) obtained from the MIROC simulation and satellite retrievals.
The model produces positive values of <inline-formula><mml:math display="inline"><mml:mrow><mml:mi>d</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi>ln⁡</mml:mi><mml:mi mathvariant="normal">LWP</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mo>/</mml:mo><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi>d</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi>ln⁡</mml:mi><mml:msub><mml:mi>N</mml:mi><mml:mtext>c</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>
almost everywhere across the globe in both non-precipitating and precipitating
cases, which indicates that the LWP systematically increases with an
increasing aerosol burden. Even when the model applies AOD or hygroscopic
<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mtext>a</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> burden as an aerosol proxy instead of <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mtext>c</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>, we obtain the similar
results (i.e., globally enhanced LWP). This result is expected from the model
parameterization of the cloud lifetime effect (Eq. <xref ref-type="disp-formula" rid="Ch1.E1"/>), which
monotonically delays the onset of precipitation in polluted conditions. This
is also a characteristic common to other GCMs, as reported in a recent study
<xref ref-type="bibr" rid="bib1.bibx17" id="paren.57"/>. In contrast, the satellite-derived LWP susceptibility has a
coherent geographical pattern that includes both increasing and decreasing
responses, which is quite different from the model results. The decreasing
response occurs over the tropics and subtropics where more convective cloud
is dominant. The increasing response is apparent mainly over the midlatitudes
and regions where low clouds are dominant <xref ref-type="bibr" rid="bib1.bibx26" id="paren.58"/>.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F3"><caption><p>Global mean susceptibility (60<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> S–60<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N) of <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mtext>c</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>,
<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mtext>e</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>, and the LWP to <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mtext>c</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>. The MIROC result is shown in orange and the
A-Train observation is in blue.</p></caption>
          <?xmltex \igopts{width=241.848425pt}?><graphic xlink:href="https://acp.copernicus.org/articles/16/15413/2016/acp-16-15413-2016-f03.pdf"/>

        </fig>

      <p>Nevertheless, it should be noted that Fig. <xref ref-type="fig" rid="Ch1.F2"/>c captures the
horizontal distribution of LWP susceptibility, whose pattern is very similar
to observations. That is, the relationship becomes weaker towards the
tropics, although the sign is still different. One of the possible mechanisms
is the dominance of cloud dynamical processes with high natural variability
over tropical and/or subtropical oceans rather than microphysical modifications by
aerosols <xref ref-type="bibr" rid="bib1.bibx42 bib1.bibx43" id="paren.59"/>. The same processes observed from
satellites could be at work in the model, and hence it might be related to
the parameterization of subgrid-scale variability. However, this is not
always true, particularly in non-precipitating cases (Fig. <xref ref-type="fig" rid="Ch1.F2"/>a),
so we must interpret the mechanisms carefully with further analysis in
future.</p>
      <p>Figure <xref ref-type="fig" rid="Ch1.F2"/>b and d show that the geographical
patterns are qualitatively similar between the non-precipitating and
precipitating conditions, whereas the contrast between the two is slightly
different. More specifically, the value of <inline-formula><mml:math display="inline"><mml:mrow><mml:mi>d</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi>ln⁡</mml:mi><mml:mi mathvariant="normal">LWP</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mo>/</mml:mo><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi>d</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi>ln⁡</mml:mi><mml:msub><mml:mi>N</mml:mi><mml:mtext>c</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> is smaller in the precipitating condition than in the
non-precipitating case, which implies a smaller effect of aerosols when
precipitation occurs. However, it is noteworthy that the positive response of
<inline-formula><mml:math display="inline"><mml:mrow><mml:mi>d</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi>ln⁡</mml:mi><mml:mi mathvariant="normal">LWP</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mo>/</mml:mo><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi>d</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi>ln⁡</mml:mi><mml:msub><mml:mi>N</mml:mi><mml:mtext>c</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> in the non-precipitating condition has
a negative value in the precipitating conditions over East Asia, the eastern
United States, and Europe, where the anthropogenic aerosol burden is severe.
This suggests that aerosols act to prolong the cloud lifetime in
non-precipitating conditions, while they enhance cloud evaporation or can be
a precipitation driver in precipitating conditions which ultimately result in
less cloud water. These two competing mechanisms are reasonably consistent
with theories suggested by recent studies
<xref ref-type="bibr" rid="bib1.bibx60 bib1.bibx48 bib1.bibx31" id="paren.60"/>, which propose the existence of a
buffering effect in the cloud system that results in smaller-magnitude
aerosol–cloud interactions. These comparisons suggest that the model does
not appropriately represent the buffering effect which compensates for the
positive responses of the LWP to aerosol perturbations. Current GCMs which
use similar parameterization frameworks (e.g., autoconversion) therefore
inherently overestimate the aerosol indirect effect as reported by previous
studies <xref ref-type="bibr" rid="bib1.bibx47 bib1.bibx77 bib1.bibx15" id="paren.61"/>.</p>
      <p>Figure <xref ref-type="fig" rid="Ch1.F3"/> summarizes the relationship among the
“process-oriented metrics” corresponding to each term in Eq. (<xref ref-type="disp-formula" rid="Ch1.E2"/>). The global mean susceptibilities (averaged from
60<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> S to 60<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N) for each term were calculated from the individual
susceptibility in each grid box in which more than 10 warm cloud samples were
obtained, which contributed to the reduction of statistical noise.</p>
      <p>The cloud susceptibility of <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mtext>c</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> to <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mtext>c</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> in MIROC is approximately
twice as large as in the A-Train results. The significant bias is decomposed
into contributions due to the “albedo effect” <inline-formula><mml:math display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mi>d</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi>ln⁡</mml:mi><mml:msub><mml:mi>r</mml:mi><mml:mtext>e</mml:mtext></mml:msub><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mo>/</mml:mo><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi>d</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi>ln⁡</mml:mi><mml:msub><mml:mi>N</mml:mi><mml:mtext>c</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> and the “lifetime effect” <inline-formula><mml:math display="inline"><mml:mrow><mml:mi>d</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi>ln⁡</mml:mi><mml:mi mathvariant="normal">LWP</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mo>/</mml:mo><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi>d</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi>ln⁡</mml:mi><mml:msub><mml:mi>N</mml:mi><mml:mtext>c</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>.
Although the former is underestimated in the model compared with A-Train
estimations, its sign is positive and consistent with observations. The
overestimation of <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mtext>c</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>-susceptibility in the model is therefore
attributed to a positive response of the LWP, which is in stark contrast to
the slight negative responses in satellite observations. <xref ref-type="bibr" rid="bib1.bibx17" id="text.62"/>
reported a wide diversity in the relationship between the LWP and <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mtext>c</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>
among nine AeroCom GCMs, with all models showing an enhanced response of LWP
to increased <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mtext>c</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>. This further causes uncertainties in the estimation of
radiative forcing <xref ref-type="bibr" rid="bib1.bibx17 bib1.bibx13" id="paren.63"/>.</p>
      <p>As Figs. <xref ref-type="fig" rid="Ch1.F2"/> and <xref ref-type="fig" rid="Ch1.F3"/> indicate, the discrepancy in the
LWP response between the model and observations can be a critical source of
model uncertainty, which causes a bias in climate responses via the
aerosol–cloud–precipitation–climate interaction.</p>
</sec>
<sec id="Ch1.S3.SS3">
  <title>Dependency of LWP responses on meteorology</title>
      <p>Another key question regarding the LWP response for aerosol perturbations is
how and to what extent it depends on macrophysics such as cloud regimes and
thermodynamic conditions in the real atmosphere. Recent studies have
suggested that the source of uncertainty in the LWP response could be
attributed to differences in meteorology, different cloud types and regimes,
or more theoretical reasons, based on satellite observations
<xref ref-type="bibr" rid="bib1.bibx55 bib1.bibx8" id="paren.64"/>, large-eddy simulation (LES;
<xref ref-type="bibr" rid="bib1.bibx31 bib1.bibx50" id="altparen.65"/>), and GCM intercomparison
<xref ref-type="bibr" rid="bib1.bibx77 bib1.bibx86" id="paren.66"/>.</p>
      <p>To address this question, we examine the dependency of the LWP susceptibility
on both column maximum radar reflectivity (<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>Z</mml:mi><mml:mtext>max</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>) and LTS as shown in
Fig. <xref ref-type="fig" rid="Ch1.F4"/>. Given that the horizontal axis characterizes the rain
regime (i.e., non-precipitating, drizzling, or precipitating) and the
vertical axis represents the thermodynamical stability conditions (i.e.,
unstable, intermediate, or stable), the diagram illustrates how the LWP
response to perturbed aerosols varies as a function of both rain
characteristics and stability conditions, thus providing a way to classify
cloud susceptibility according to macroscopic and meteorological conditions.</p>
      <p>Figure <xref ref-type="fig" rid="Ch1.F4"/> clearly shows a systematic variation of the cloud
susceptibility under the two conditions. Positive responses of the LWP to
<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mtext>c</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> are dominant in the non-precipitating and stable environments, while
negative responses can be seen in precipitating and unstable conditions. The
top-left region in the diagram corresponds to a stratocumulus regime in the
marine boundary layer. Because this type of cloud typically produces light
precipitation (i.e., drizzle; <xref ref-type="bibr" rid="bib1.bibx84" id="altparen.67"/>) rather than heavy
precipitation it depletes a large amount of cloud water, and the aerosols
ingested into this type of cloud effectively act to enhance cloud water
storage, resulting in a positive response of LWP to an increased aerosol
loading. In contrast, the right-bottom region in the diagram corresponds to a
more convective cumulus regime, which is present mainly over the tropics.
This type of cloud is characterized by a relatively fast precipitation
timescale <xref ref-type="bibr" rid="bib1.bibx55" id="paren.68"/>, and is favorable for cloud water
evaporation due to the larger extent of entrainment mixing <xref ref-type="bibr" rid="bib1.bibx53" id="paren.69"/>,
which results in negative responses of the LWP.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F4"><caption><p>Susceptibility matrix of the LWP response to <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mtext>c</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> as a function
of column maximum radar reflectivity (<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>Z</mml:mi><mml:mtext>max</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>) and lower-tropospheric
stability (LTS) based on A-Train satellite data.</p></caption>
          <?xmltex \igopts{width=227.622047pt}?><graphic xlink:href="https://acp.copernicus.org/articles/16/15413/2016/acp-16-15413-2016-f04.pdf"/>

        </fig>

      <p>It is interesting that there is a positive correlation in the top-right
region even though precipitation occurs. One possible interpretation of this
is that the water-vapor supply is dominant over the loss of cloud water by
precipitation, and this type of cloud may correspond to the sustained frontal
precipitation (precipitating nimbostratus) systems found mainly over
midlatitude oceanic regions, where water vapor is abundant. In pristine and clean
environments, referred to as “aerosol-limited” conditions
<xref ref-type="bibr" rid="bib1.bibx28" id="paren.70"/>, aerosols ingested into clouds will tend to store the cloud
water but also simultaneously produce more rain due to abundant water
mass. We note that it is just a speculation at this stage, and it might be
related to background aerosol number and environmental conditions (cf. Sect. 4 for more discussion). It is also noteworthy that the bottom-left region
displays negative susceptibilities even though precipitation does not occur.
Non-precipitating clouds in a significantly unstable environment would
correspond to inland and/or daytime cumulus. This tendency agrees with the results
of a previous study <xref ref-type="bibr" rid="bib1.bibx53" id="paren.71"/> that focused on the non-precipitating
cumulus regime, and suggests a mechanism whereby the LWP decreases with
increased aerosol loading via evaporation–entrainment feedback. This results
in a loss of cloud water without precipitation.</p>
      <p>Although the model version of the LWP-susceptibility diagram is not shown, it
will indicate a positive value in the matrix overall, as is obvious from Fig. <xref ref-type="fig" rid="Ch1.F2"/>. The mechanisms proposed above must be confirmed by more
detailed examinations using GCM and CRM with satellite simulators, or using
high-resolution process modeling, such as LES, in future studies. However,
the observation-based findings described above strongly suggest that rigorous
studies focusing on macrophysical conditions, including regional
characteristics of meteorological factors, in addition to microphysical
conditions, are indispensable for better understanding the response of the
aerosol–cloud–precipitation interaction.</p>
</sec>
</sec>
<sec id="Ch1.S4" sec-type="conclusions">
  <title>Summary and discussion</title>
      <p>We explored the source of discrepancy in the aerosol–cloud–precipitation
interaction for warm clouds between an aerosol–climate model and A-Train
satellite retrieval. The instantaneous model output was analyzed using as
many samples as possible to provide reliable statistics and fair comparisons
with satellite observations.</p>
      <p>We found critical biases in the model in the response of the LWP to aerosol
perturbations. The model predicted a monotonic increase in the LWP across the
globe, in contrast to the observations that clearly showed a regional
variation of the LWP response that either increased or decreased with an
increasing aerosol loading. This variability in cloud susceptibility observed
by the A-Train was closely related to differences in meteorological factors,
such as cloud regimes and thermodynamic conditions. For example, stratiform
clouds under stable conditions had a tendency to increase the LWP given
aerosol perturbations, while cumulus clouds over an unstable environment
tended to decrease the LWP as the aerosol loading increased. The
bidirectional responses of LWP (both positive and negative) found in
satellite observations in different aerosol concentrations might be related
to the concept of “optimal aerosol concentration (<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mtext>op</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>)”, recently
suggested by <xref ref-type="bibr" rid="bib1.bibx10 bib1.bibx11" id="text.72"/>. More specifically, in case of <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mtext>a</mml:mtext></mml:msub><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mo>&lt;</mml:mo><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msub><mml:mi>N</mml:mi><mml:mtext>op</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>, clouds tend to be deeper with larger liquid mass, referred
to as cloud invigoration <xref ref-type="bibr" rid="bib1.bibx28" id="paren.73"><named-content content-type="pre">e.g.,</named-content></xref>, for increased aerosol
loading, whereas the case of <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mtext>a</mml:mtext></mml:msub><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mo>&gt;</mml:mo><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msub><mml:mi>N</mml:mi><mml:mtext>op</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> would be favorable for
cloud suppression due to enhanced entrainment and evaporation. This could
lead the bidirectional LWP susceptibilities, although we cannot mention the
exact mechanisms at this stage because <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mtext>op</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> also depends on both cloud
geometric scale and environmental conditions
<xref ref-type="bibr" rid="bib1.bibx28 bib1.bibx10 bib1.bibx11" id="paren.74"/>.</p>
      <p>This can explain why previous studies have reported conflicting results for
the LWP response, with either an increase or decrease with increasing aerosol
loading <xref ref-type="bibr" rid="bib1.bibx52 bib1.bibx3 bib1.bibx37" id="paren.75"><named-content content-type="pre">e.g.,</named-content></xref>. Previous
studies have focused on different study regions and/or targets, which has
resulted in different cloud responses due to the different mechanisms of
aerosol–cloud–precipitation interaction. This means that global-mean cloud
susceptibility is not very meaningful in constraining the
aerosol–cloud–precipitation interaction. Future studies should consider the
regional dependence of the susceptibility metrics <xref ref-type="bibr" rid="bib1.bibx72" id="paren.76"/>.</p>
      <p>The monotonic increase in the LWP with increasing aerosol loading in the
model is attributed to the autoconversion scheme, which assumes only
suppression of rainwater generation to account for the traditional cloud
lifetime effect without its compensation, and does not take meteorological
conditions into account. Mechanisms that can decrease the LWP in polluted
conditions, such as the enhancement of evaporation due to entrainment mixing
<xref ref-type="bibr" rid="bib1.bibx53 bib1.bibx50" id="paren.77"/>, are not incorporated in our model. This means
that the model fails to represent the buffering effect for the
aerosol–cloud–precipitation interaction <xref ref-type="bibr" rid="bib1.bibx60" id="paren.78"/>. Moreover, the
model overestimates <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mtext>conv</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> around low LWPs compared with A-Train
satellite retrievals due to uncertainties in process rate parameterization
<xref ref-type="bibr" rid="bib1.bibx81" id="paren.79"/>. This is evidence that the autoconversion in the model is
too fast, which results in the LWP having a high dependency on the <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mtext>c</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>.
This bias in the model is consistent with a previous study that reported a
higher LWP susceptibility in GCMs due to their diagnostic treatment of
rainwater <xref ref-type="bibr" rid="bib1.bibx77" id="paren.80"/>.</p>
      <p>In future studies, the aerosol–cloud–precipitation framework must be
expanded to represent the effect of environmental conditions in a flexible
manner, in addition to the microphysics. Current microphysical frameworks
without such macrophysical aspects bring highly sensitive aerosol–cloud
interactions, although they vary to some extent depending on the
autoconversion scheme <xref ref-type="bibr" rid="bib1.bibx14 bib1.bibx65 bib1.bibx38" id="paren.81"/>.
<xref ref-type="bibr" rid="bib1.bibx17" id="text.82"/> also reported a wide diversity in the LWP response to
<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mtext>c</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> among various GCMs, and concluded that their inconsistency could
mainly be attributed to their different representations of the autoconversion
process. However, it is also true that different choices of microphysical
scheme alone do not significantly improve the model biases in both cloud
physics and cloud radiative effects <xref ref-type="bibr" rid="bib1.bibx38" id="paren.83"/>, and these two
requirements sometimes contradict each other <xref ref-type="bibr" rid="bib1.bibx63" id="paren.84"/>. This is due
to the arbitrary nature of tuning and assumptions (e.g., artificial threshold
parameters, diagnostic treatment of rain), which is a bottleneck in GCMs
<xref ref-type="bibr" rid="bib1.bibx24 bib1.bibx47 bib1.bibx18" id="paren.85"/>. Recently, a fundamental model
improvement was achieved by introducing a prognostic precipitation framework
<xref ref-type="bibr" rid="bib1.bibx16 bib1.bibx49" id="paren.86"/>, which represents important progress in
process representations for more realistic cloud and precipitation
microphysics. This improvement is expected to overcome some of the common
problems in GCMs, such as the overestimation of the aerosol indirect effect
and spurious light rain <xref ref-type="bibr" rid="bib1.bibx76 bib1.bibx16 bib1.bibx49" id="paren.87"/>.</p>
      <p>Furthermore, a representation of subgrid-scale fluctuations has also been
critical problem in GCMs. Although the magnitude as well as sign of
LWP susceptibility differs between the model and observations, the horizontal
pattern is similar in precipitating conditions. The parameterization of
subgrid-scale variability may partly contribute to the weakening of the aerosol roles
by capturing the large natural variability of clouds, especially over
tropical and/or subtropical oceans <xref ref-type="bibr" rid="bib1.bibx42 bib1.bibx43" id="paren.88"/>, which would lead
to a more realistic representation of cloud dynamical processes. For example,
<xref ref-type="bibr" rid="bib1.bibx21 bib1.bibx22" id="text.89"/> showed that both positive and negative LWP responses
can be represented in even a GCM framework, by the PDF-based macrophysics
parameterization, called “Cloud Layers Unified By Binormals
<xref ref-type="bibr" rid="bib1.bibx30" id="paren.90"><named-content content-type="pre">CLUBB;</named-content></xref>”. <xref ref-type="bibr" rid="bib1.bibx32" id="text.91"/> estimated a weighting
factor of process rate equations to consider the subgrid effects based on
A-Train retrievals unless the accretion process is significantly underestimated.
The interaction between microphysics and subgrid-scale dynamics
(microphysics–dynamics interactions) in GCMs is therefore one of the
indispensable processes for incorporating buffering effects and for improving
model physics as a whole.</p>
      <p>Although this study focused only on warm-phase clouds, our findings regarding
different cloud responses to aerosol perturbations between GCMs and satellite
observations will assist future model development for more accurate climate
simulations. Further studies should also contain an extension of the research
target from liquid to mixed and/or iced clouds, and from a process-level to a cloud
system to understand the whole cloud system response to aerosol
perturbations, taking into account the buffered system morphology.</p>
</sec>
<sec id="Ch1.S5">
  <title>Data availability</title>
      <p>The original CloudSat data products can be obtained from the CloudSat Data Processing Center at CIRA, Colorado State University
(<uri>http://www.cloudsat.cira.colostate.edu</uri>). The CloudSat and MIROC–SPRINTARS data used in this study are available on request
from the corresponding author (michibata@riam.kyushu-u.ac.jp).</p>
</sec>

      
      </body>
    <back><notes notes-type="authorcontribution">

      <p>Takuro Michibata proposed the research. Takuro Michibata and Toshihiko Takemura designed the research. Takuro Michibata, Toshihiko Takemura, Kentaroh Suzuki, and Yousuke Sato performed
the research. Toshihiko Takemura, Kentaroh Suzuki, and Yousuke Sato contributed new analytic tools; Takuro Michibata analyzed the data. Takuro Michibata and Kentaroh Suzuki wrote the paper.</p>
  </notes><notes notes-type="competinginterests">

      <p>The authors declare that they have no conflict of interest.</p>
  </notes><ack><title>Acknowledgements</title><p>This study was supported by JSPS KAKENHI Grant-in-Aid for Research Fellows
(JP15J05544) and Scientific Research (JP15K12190), the Environment Research
and Technology Development Fund (S-12-3) of the Ministry of the Environment,
Japan, and the Collaborative Research Program of Research Institute for
Applied Mechanics, Kyushu University. Kentaroh Suzuki was supported by NOAA's
Climate Program Office's Modeling, Analysis, Predictions, and Projections
program with grant number NA15OAR4310153. Simulations by MIROC–SPRINTARS were
executed with the SX-9/ACE supercomputer system of the National Institute for
Environmental Studies, Japan. The authors would like
to express their heartfelt gratitude to the CloudSat science team. Finally, the authors thank
two anonymous reviewers for providing constructive suggestions and comments,
as well as Karsten Peters for his insightful discussion, which have
significantly improved the paper.
<?xmltex \hack{\newline}?><?xmltex \hack{\newline}?>
Edited by: P. Stier<?xmltex \hack{\newline}?>
Reviewed by: two anonymous referees</p></ack><ref-list>
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    </app></app-group></back>
    <!--<article-title-html>The source of discrepancies in aerosol–cloud–precipitation interactions between GCM and A-Train retrievals</article-title-html>
<abstract-html><p class="p">Aerosol–cloud interactions are one of the most uncertain processes in
climate models due to their nonlinear complexity. A key complexity arises
from the possibility that clouds can respond to perturbed aerosols in two
opposite ways, as characterized by the traditional “cloud lifetime”
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LWP from the A-Train varies from region to region. The satellite-observed
response of the LWP is closely related to meteorological and/or
macrophysical factors, in addition to the microphysics. The model does not reproduce this
variability of cloud susceptibility (i.e., sensitivity of LWP to perturbed
aerosols) because the parameterization of the autoconversion process assumes
only suppression of rain formation in response to increased cloud droplet
number, and does not consider macrophysical aspects that serve as a mechanism
for the negative responses of the LWP via enhancements of evaporation and
precipitation. Model biases are also found in the precipitation microphysics,
which suggests that the model generates rainwater readily even when little
cloud water is present. This essentially causes projections of
unrealistically frequent and light rain, with high cloud susceptibilities to
aerosol perturbations.</p></abstract-html>
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