<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE article PUBLIC "-//NLM//DTD Journal Publishing with OASIS Tables v3.0 20080202//EN" "https://jats.nlm.nih.gov/nlm-dtd/publishing/3.0/journalpub-oasis3.dtd">
<article xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:oasis="http://docs.oasis-open.org/ns/oasis-exchange/table" xml:lang="en" dtd-version="3.0" article-type="research-article"><?xmltex \bartext{ACP Letters}?>
  <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-23-8259-2023</article-id><title-group><article-title>Detection of large-scale cloud microphysical changes within a major shipping corridor after implementation of the International Maritime
Organization 2020 <?xmltex \hack{\break}?>fuel sulfur regulations</article-title><alt-title>Detection of large-scale cloud microphysical changes</alt-title>
      </title-group><?xmltex \runningtitle{Detection of large-scale cloud microphysical changes}?><?xmltex \runningauthor{M. S. Diamond}?>
      <contrib-group>
        <contrib contrib-type="author" corresp="yes">
          <name><surname>Diamond</surname><given-names>Michael S.</given-names></name>
          <email>msdiamond@fsu.edu</email>
        <ext-link>https://orcid.org/0000-0003-2147-5921</ext-link></contrib>
        <aff id="aff1"><institution>Department of Earth, Ocean and Atmospheric Science, Florida State
University, Tallahassee, FL 32306, USA</institution>
        </aff>
      </contrib-group>
      <author-notes><corresp id="corr1">Michael S. Diamond (msdiamond@fsu.edu)</corresp></author-notes><pub-date><day>25</day><month>July</month><year>2023</year></pub-date>
      
      <volume>23</volume>
      <issue>14</issue>
      <fpage>8259</fpage><lpage>8269</lpage>
      <history>
        <date date-type="received"><day>11</day><month>May</month><year>2023</year></date>
           <date date-type="rev-request"><day>22</day><month>May</month><year>2023</year></date>
           <date date-type="rev-recd"><day>20</day><month>June</month><year>2023</year></date>
           <date date-type="accepted"><day>29</day><month>June</month><year>2023</year></date>
      </history>
      <permissions>
        <copyright-statement>Copyright: © 2023 Michael S. Diamond</copyright-statement>
        <copyright-year>2023</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/acp-23-8259-2023.html">This article is available from https://acp.copernicus.org/articles/acp-23-8259-2023.html</self-uri><self-uri xlink:href="https://acp.copernicus.org/articles/acp-23-8259-2023.pdf">The full text article is available as a PDF file from https://acp.copernicus.org/articles/acp-23-8259-2023.pdf</self-uri>
      <abstract><title>Abstract</title>

      <p id="d1e81">New regulations from the International Maritime
Organization (IMO) limiting sulfur emissions from the shipping industry are
expected to have large benefits in terms of public health but may come with
an undesired side effect: acceleration of global warming as the
climate-cooling effects of ship pollution on marine clouds are diminished.
Previous work has found a substantial decrease in the detection of ship
tracks in clouds after the IMO 2020 regulations went into effect, but changes
in large-scale cloud properties have been more equivocal. Using a
statistical technique that estimates counterfactual fields of what
large-scale cloud and radiative properties within an isolated shipping
corridor in the southeastern Atlantic would have been in the absence of
shipping, we confidently detect a reduction in the magnitude of cloud
droplet effective radius decreases within the shipping corridor and find
evidence for a reduction in the magnitude of cloud brightening as well. The
instantaneous radiative forcing due to aerosol–cloud interactions from the
IMO 2020 regulations is estimated as <inline-formula><mml:math id="M1" display="inline"><mml:mi>O</mml:mi></mml:math></inline-formula>(1 W m<inline-formula><mml:math id="M2" 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>) within the shipping
corridor, lending credence to global estimates of <inline-formula><mml:math id="M3" display="inline"><mml:mi>O</mml:mi></mml:math></inline-formula>(0.1 W m<inline-formula><mml:math id="M4" 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>). In
addition to their geophysical significance, our results also provide
independent evidence for general compliance with the IMO 2020 regulations.</p>
  </abstract>
    
<funding-group>
<award-group id="gs1">
<funding-source>Florida State University</funding-source>
<award-id>N/A (new faculty startup)</award-id>
</award-group>
</funding-group>
</article-meta>
  </front>
<body>
      

<sec id="Ch1.S1" sec-type="intro">
  <label>1</label><title>Introduction and approach</title>
      <p id="d1e131">Since 1 January 2020, International Maritime Organization (IMO) Marine
Environment Protection Committee (MEPC) regulations have limited sulfur in
marine fuels from 3.5 % by mass to 0.5 % or required exhaust gas
cleaning systems (scrubbers) to achieve an equivalent reduction in sulfur
oxide (SO<inline-formula><mml:math id="M5" display="inline"><mml:msub><mml:mi/><mml:mi>x</mml:mi></mml:msub></mml:math></inline-formula>) pollution (IMO, 2019). These IMO 2020 fuel
sulfur regulations and the resulting decrease in sulfate aerosol (airborne
particulates) are expected to have large benefits to public health
(Partanen et al., 2013; Sofiev et al., 2018; Zhang et al., 2021). They
are also expected to have an undesired side effect, however: as sulfate
aerosol cools the climate by reflecting sunlight directly and indirectly via
changing cloud properties, the IMO 2020 SO<inline-formula><mml:math id="M6" display="inline"><mml:msub><mml:mi/><mml:mi>x</mml:mi></mml:msub></mml:math></inline-formula> reductions may accelerate
global warming.</p>
      <p id="d1e152"><?xmltex \hack{\newpage}?>Shipping effects on clouds were first identified in the mid-1960s in
satellite imagery of ship tracks,
or curvilinear cloud perturbations following individual ships (Conover, 1966; Twomey et al., 1968). For the same amount of liquid water within a cloud, increasing aerosol increases the cloud droplet number concentration (<inline-formula><mml:math id="M7" display="inline"><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) and decreases the cloud-top effective radius (<inline-formula><mml:math id="M8" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>), brightening the clouds (Twomey, 1974, 1977). Cloud macrophysical adjustments to this aforementioned Twomey effect have been observed within ship tracks as well and can reinforce the microphysical brightening effect by suppressing drizzle (Albrecht, 1989; Goren and Rosenfeld, 2012) or counteract it by enhancing entrainment  (Chen et al., 2012; Coakley and Walsh, 2002; Toll et al., 2019). Understanding how much greenhouse gas warming is masked by these aerosol–cloud interactions from shipping and other forms of pollution is the la<?pagebreak page8260?>rgest source of uncertainty in quantifying present-day anthropogenic radiative forcing (Forster et al., 2021).</p>
      <p id="d1e178">Although ship tracks have long served as “natural experiments” for testing
hypotheses about aerosol–cloud interactions in cases of clear causality
(Christensen et al.,
2022), until recently, attempts to observationally assess
regional- to global-scale cloud perturbations and forcing from shipping have
found negligible  (Schreier et al., 2007) or null effects  (Peters
et al., 2011) due to the small fraction of ships that form easily
identifiable tracks and the large background variability in cloud
properties. New methods using machine learning have identified many times
more ship tracks than has been possible with manual identification
(Watson-Parris et al., 2022; Yuan et al., 2022, 2019), and
analyses tracking air masses from ship locations have shown that cloud
adjustments differ systematically between easily identifiable and
“invisible” ship tracks  (Manshausen et al., 2022). Using some of
these newer methods, it has been shown that ship track occurrence decreased
regionally after the introduction of emission control areas around North
America and Europe and then globally after the IMO 2020 regulations went
into effect   (Gryspeerdt et al., 2019; Watson-Parris et al., 2022; Yuan et
al., 2022). Large-scale changes in cloud microphysical and macrophysical
properties have been more equivocal, however. Yuan et al. (2022)
found smaller <inline-formula><mml:math id="M9" display="inline"><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> increases within ship tracks after the IMO 2020
regulations, as expected, but, paradoxically, greater <inline-formula><mml:math id="M10" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> decreases than
before and no difference in cloud brightness.
Watson-Parris et al. (2022) did not find evidence
for a change in global or regional <inline-formula><mml:math id="M11" display="inline"><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> after the IMO 2020 regulations
despite the clear decrease in ship tracks, with a possible exception in the
southeastern Atlantic.</p>
      <p id="d1e214">In this work, we assess the detectability of large-scale cloud perturbations
from the IMO 2020 regulations by revisiting an alternate solution to the
limitations of “bottom-up” methods tracking individual ship tracks: a
“top-down” statistical approach developed by  Diamond et al. (2020),
hereafter D20, to identify regional-scale cloud perturbations within a
shipping corridor in the southeastern Atlantic Ocean basin. A unique
meteorological setup makes that region ideal for estimating causal aerosol
effects: near-surface winds blow parallel to the shipping corridor and
closely constrain the pollution, which also happens to intersect a major
stratocumulus cloud deck. D20 used a universal kriging method (see Zimmerman
and Stein, 2010, and references therein) to estimate counterfactual fields
of cloud properties and radiation in the absence of the shipping corridor
based on the observed spatial statistics of nearby, non-shipping-affected
grid boxes. They found significant increases in <inline-formula><mml:math id="M12" display="inline"><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and cloud albedo (a
measure of cloud reflectivity) and decreases in <inline-formula><mml:math id="M13" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> within the
stratocumulus deck but estimated that several years' worth of data were
needed to detect a clear signal. Thus, it is possible that the effect of the
IMO 2020 regulations will have just become detectable using their method.</p>
      <p id="d1e240">Here, we apply an updated version of the D20 universal kriging algorithm to
satellite retrievals of <inline-formula><mml:math id="M14" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and overcast albedo (<inline-formula><mml:math id="M15" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">cld</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>;
top-of-atmosphere albedo when clouds are present) from the Clouds and the
Earth's Radiant Energy System (CERES) Single Scanner Footprint (SSF) product
for the Terra satellite (Loeb et al., 2018; Minnis et al., 2011). The
reader is referred to Methods in Appendix A for further details about the
data, universal kriging algorithm, and significance tests. Although D20
found a substantial decrease in cloud liquid water path within the corridor
during the afternoon, no significant cloud macrophysical adjustments were
found in the morning. We therefore interpret any changes in <inline-formula><mml:math id="M16" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and
<inline-formula><mml:math id="M17" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">cld</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> using the Terra record (observations at <inline-formula><mml:math id="M18" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 10:30
local time) as being dominated by the Twomey effect. We focus on both the
austral spring season (SON; September–October–November), which features
the strongest shipping signal (likely due to a combination of favorable
meteorology and lower background <inline-formula><mml:math id="M19" display="inline"><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>;  Grosvenor et al., 2018),
and the annual mean (ANN), which averages a greater number of observations
and thus should minimize noise. For a variable <inline-formula><mml:math id="M20" display="inline"><mml:mi>X</mml:mi></mml:math></inline-formula>, the “factual” or observed
value in the presence of the shipping corridor is referred to as “Ship”
(<inline-formula><mml:math id="M21" display="inline"><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mi mathvariant="normal">Ship</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>), the counterfactual value in the absence of shipping obtained
via kriging is referred to as “NoShip” (<inline-formula><mml:math id="M22" display="inline"><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mi mathvariant="normal">NoShip</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, and the Ship–NoShip
difference is signified as <inline-formula><mml:math id="M23" display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>X</mml:mi></mml:mrow></mml:math></inline-formula> and is interpreted as the effect due to
the presence of the shipping corridor.</p>
</sec>
<sec id="Ch1.S2">
  <label>2</label><title>Results</title>
      <p id="d1e355">An unambiguous decrease in the magnitude of the <inline-formula><mml:math id="M24" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> perturbation within
the shipping corridor is evident in the post-regulation (2020–2022) data
compared to the pre-2020 climatology (2002–2019) and the immediately
preceding 3-year period (2017–2019) during austral spring (Fig. 1).
Although several significant grid boxes (observations falling outside the
95 % confidence interval of the counterfactual) remain in the south of the
domain, and thus some level of continued shipping influence is detected (as
indicated by field significance at the <inline-formula><mml:math id="M25" display="inline"><mml:mo>≪</mml:mo></mml:math></inline-formula> 0.05 level), the microphysical
changes are smaller and less clearly tied to the corridor; the signal is
completely lost further north. Similar results are found for the annual mean
values (Supplement Fig. S1), albeit with a clearer continued effect of shipping in the
2020–2022 data.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F1" specific-use="star"><?xmltex \currentcnt{1}?><?xmltex \def\figurename{Figure}?><label>Figure 1</label><caption><p id="d1e378">Maps of factual (observed) and counterfactual values and their
difference for austral spring cloud-top effective radius for the pre-2020
climatology <bold>(a–c)</bold>, the immediately pre-regulation 3-year period 2017–2019 <bold>(d–f)</bold>, and the immediate post-regulation 3-year period 2020–2022 <bold>(g–i)</bold>.
The analysis domain of 18 to 8<inline-formula><mml:math id="M26" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> S, 13<inline-formula><mml:math id="M27" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> W to
8<inline-formula><mml:math id="M28" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> E is outlined in black. Grid points for which the observed
values fall outside the 95 % confidence interval obtained via kriging are
indicated by white dots, and the corresponding field significance values are
reported in <bold>(c)</bold>, <bold>(f)</bold>, and <bold>(i)</bold>.</p></caption>
        <?xmltex \igopts{width=398.338583pt}?><graphic xlink:href="https://acp.copernicus.org/articles/23/8259/2023/acp-23-8259-2023-f01.png"/>

      </fig>

      <p id="d1e433">The shipping perturbation in overcast albedo is less well defined than that
in the cloud microphysics, but there is still a clear perturbation in the
2002–2019 climatology and 2017–2019 data that is diminished in the
2020–2022 data in austral spring (Fig. 2). Similar results are found in the
annual mean, although the 2020–2022 change is more ambiguous from visual
inspection alone (Fig. S2). Lower background <inline-formula><mml:math id="M29" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">cld</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> values in 2020–2022,
particularly in the annual mean (Fig. S2g), may be related to unusually warm
sea surface temperatures (Figs. S3–S4); as dimmer clouds are relatively more
susceptible to aerosol perturbations, this effect may partially obscure<?pagebreak page8261?> the
decrease in cloud brightening from the IMO 2020 regulations.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F2" specific-use="star"><?xmltex \currentcnt{2}?><?xmltex \def\figurename{Figure}?><label>Figure 2</label><caption><p id="d1e450">As in Fig. 1 but for austral spring overcast albedo.</p></caption>
        <?xmltex \igopts{width=398.338583pt}?><graphic xlink:href="https://acp.copernicus.org/articles/23/8259/2023/acp-23-8259-2023-f02.png"/>

      </fig>

      <p id="d1e459">To assess how anomalous the post-regulation 2020–2022 shipping perturbation
values are, we compare them to those from prior 3-year periods by
averaging over a core shipping corridor region (see Methods in Appendix A)
and, to minimize effects from changing background conditions, also calculate
perturbations as relative differences (100 % <inline-formula><mml:math id="M30" display="inline"><mml:mo>⋅</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M31" display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>X</mml:mi><mml:mo>/</mml:mo><mml:msub><mml:mi>X</mml:mi><mml:mi mathvariant="normal">Ship</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>). Full
results are reported in Table S1 and summarized in Fig. 3. For the austral
spring <inline-formula><mml:math id="M32" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> perturbations, 2020–2022 is unprecedentedly weak (Fig. 3a)
and does not overlap any prior period's value within their 95 % confidence
intervals (Table S1 in the Supplement). The separation between 2020–2022 and any other
period's values is not as clear for austral spring <inline-formula><mml:math id="M33" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">cld</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> (Fig. 3b),
although the 2020–2022 perturbation values are the lowest on record and are
the only period for which the effect is not distinguishable from zero at the
95 % confidence level (Table S1). For the annual mean <inline-formula><mml:math id="M34" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>
perturbations, the 2020–2022 values are lower than any other period and the
difference with the climatological value is much larger than for any other
period, although the separation is not as clear as for austral spring (Fig. 3c). While the annual mean <inline-formula><mml:math id="M35" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">cld</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> perturbations for 2020–2022 are also
the lowest on record, the difference from climatology is not extreme
compared to other periods (Fig. 3d).</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F3"><?xmltex \currentcnt{3}?><?xmltex \def\figurename{Figure}?><label>Figure 3</label><caption><p id="d1e533">Probability densities (via Gaussian kernel density estimation) for
the Ship–NoShip relative differences within the core shipping corridor for
austral spring <inline-formula><mml:math id="M36" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> <bold>(a)</bold>, austral spring <inline-formula><mml:math id="M37" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">cld</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> <bold>(b)</bold>, annual mean
<inline-formula><mml:math id="M38" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> <bold>(c)</bold>, and annual mean <inline-formula><mml:math id="M39" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">cld</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> <bold>(d)</bold>. The 2002–2019 climatology values
are shown as gray shading, the 3-year periods prior to the IMO 2020
regulations as colored lines, and the 2020–2022 period as black lines.
Solid, dashed, and dotted lines indicate decreasing degrees of field
significance.</p></caption>
        <?xmltex \igopts{width=241.848425pt}?><graphic xlink:href="https://acp.copernicus.org/articles/23/8259/2023/acp-23-8259-2023-f03.png"/>

      </fig>

      <p id="d1e599">To assess whether a reduction in the shipping effect after the IMO 2020
regulations went into effect is detected at various possible levels of
confidence, Table S2 reports different percentiles of the ratio of the
2020–2022 relative differences over the climatology. A decrease in the
<inline-formula><mml:math id="M40" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> perturbation is detected at greater than 99 % confidence in the
austral spring and at greater than 95 % confidence in the annual mean,
whereas decreases in the <inline-formula><mml:math id="M41" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">cld</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> perturbation are only significant at the
90 % confidence level in the austral spring and within the interquartile
range in the annual mean. We thus conclude that the effect of the IMO 2020
regulations has been clearly detected in the large-scale cloud microphysics
and that there is strong evidence for a decrease in cloud brightness,
although more years of data may be required for unequivocal detection of
changes in overcast albedo.</p>
</sec>
<sec id="Ch1.S3">
  <label>3</label><title>Discussion</title>
<sec id="Ch1.S3.SS1">
  <label>3.1</label><title>Monitoring compliance with IMO regulations</title>
      <p id="d1e639">Assessing (non)compliance with the IMO 2020 regulations is of critical
importance for ensuring that the intended public health benefits are
realized. One assessment method is<?pagebreak page8262?> to monitor the sulfur content of the
global fuel oil supply. According to data supplied to the IMO MEPC  (IMO,
2020, 2021, 2022, 2023), before 2020, the average sulfur mass content of
marine fuel oils was <inline-formula><mml:math id="M42" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 2.5 % and <inline-formula><mml:math id="M43" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 80 % of
the global fuel oil supply exceeded 0.5 %; since 2020, the average sulfur
mass content has declined to <inline-formula><mml:math id="M44" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 1 % and only <inline-formula><mml:math id="M45" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 20 % of fuel has exceeded 0.5 % (Fig. S5). These values understate
compliance, as a “carriage ban” forbids ships from carrying the remaining
noncompliant fuel oil unless they have scrubbers installed  (IMO,
2018). Geophysical monitoring via cloud changes, as has been shown in
Yuan et al. (2022) and  Watson-Parris et
al. (2022) for ship track occurrence and here for large-scale cloud
microphysical properties, offers an independent check to increase confidence
that there has been substantial compliance with the IMO 2020 regulations. As
our understanding of the cloud effects from shipping aerosol improves, it may
become possible to assess regional differences in compliance or even
compliance for individual ships, complementing other successful geophysical
monitoring programs like those for detecting ozone-depleting substances
(Montzka et al., 2018; Park et al., 2021; Rigby et al., 2019).</p>
      <p id="d1e670">Given the clear detection of cloud microphysical changes in austral spring
after the IMO 2020 regulations went into effect, it is reasonable to ask
whether advanced statistical methods are necessary for evaluating (some
level of) compliance or if simple time series (e.g., Fig. S5 of
Watson-Parris et al., 2022) would suffice. From
the time series of austral spring Ship and NoShip <inline-formula><mml:math id="M46" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> values averaged
over the southeastern Atlantic (Fig. 4), it is evident that the shipping
effect before 2020–2022 is of similar magnitude to interannual variability
in the background values and that the 2020–2022 <inline-formula><mml:math id="M47" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> values are estimated
to be the highest on record even before any IMO 2020 effect is considered.
As an estimate of what the 2020–2022 observed value would have been under a
scenario of complete noncompliance with the sulfur regulations, the average
Ship–NoShip difference from the 2002–2019 climatology is applied to the
2020–2022 NoShip value (“Noncompliance” in Fig. 4). The <inline-formula><mml:math id="M48" display="inline"><mml:mo>+</mml:mo></mml:math></inline-formula>0.1 <inline-formula><mml:math id="M49" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi></mml:mrow></mml:math></inline-formula>m
difference between the observed (Ship) value and this noncompliance
hypothetical is due to compliance with the IMO 2020 regulations. If we had
rather based our noncompliance scenario on a persistence forecast of the
2017–2019 value and then observed the value from the “true” noncompliance
estimate calculated above, we would erroneously conclude that the IMO 2020
regulations were successfully implemented and led to a <inline-formula><mml:math id="M50" display="inline"><mml:mo>+</mml:mo></mml:math></inline-formula>0.3 <inline-formula><mml:math id="M51" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi></mml:mrow></mml:math></inline-formula>m
increase in regional <inline-formula><mml:math id="M52" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>. Of course, in this latter scenario, the true
value of the difference due to IMO 2020 would have been zero and the
apparent effect only an artifact of the changing background. Caution is
therefore advised in attempting to interpret time series of large-scale
cloud properties without applying a method (like track identification or
kriging) that plausibly establishes causality.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F4"><?xmltex \currentcnt{4}?><?xmltex \def\figurename{Figure}?><label>Figure 4</label><caption><p id="d1e739">Time series of observed Ship (black circles) and mean NoShip (blue
diamonds) values averaged the southeastern Atlantic analysis domain
(18 to 8<inline-formula><mml:math id="M53" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> S, 13<inline-formula><mml:math id="M54" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> W to 8<inline-formula><mml:math id="M55" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> E) for
austral spring <inline-formula><mml:math id="M56" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>. Error bars represent 95 % confidence for the NoShip
values. A noncompliance scenario in which the IMO 2020 regulations were not
enforced and the Ship–NoShip differences in 2020–2022 were the same as for
the 2002–2019 climatology is denoted as a dark-red “x”. The dotted red
line denotes the estimated effect from compliance with the IMO 2020
regulations, calculated as the difference between the observed Ship value
and the hypothetical noncompliance value expected for no change in
2020–2022. The dotted orange line denotes the mistakenly determined effect
that would have resulted if the noncompliance scenario were true and
observed but a persistence forecast of 2017–2019 were used as the
expectation value for no change in 2020–2022.</p></caption>
          <?xmltex \igopts{width=241.848425pt}?><graphic xlink:href="https://acp.copernicus.org/articles/23/8259/2023/acp-23-8259-2023-f04.png"/>

        </fig>

</sec>
<?pagebreak page8263?><sec id="Ch1.S3.SS2">
  <label>3.2</label><title>Radiative forcing implications</title>
      <p id="d1e794">Assuming that the Terra-based <inline-formula><mml:math id="M57" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M58" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">cld</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> perturbations are dominated by the Twomey effect as in D20, it is possible to estimate the instantaneous radiative forcing due to aerosol–cloud interactions (IRF<inline-formula><mml:math id="M59" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">ACI</mml:mi></mml:msub></mml:math></inline-formula>; Forster et al., 2021) from the IMO 2020 regulations within the shipping corridor (see Methods in Appendix A). Results are shown in Fig. 5 for the 2002–2019 climatology, 2020–2022, and their difference (interpreted as the effect of the IMO 2020 regulations). The Twomey effect estimates are much better constrained for the calculations using <inline-formula><mml:math id="M60" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, but those using <inline-formula><mml:math id="M61" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">cld</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> show consistent results. The IMO 2020 regulations led to a <inline-formula><mml:math id="M62" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 2 W m<inline-formula><mml:math id="M63" 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> IRF<inline-formula><mml:math id="M64" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">ACI</mml:mi></mml:msub></mml:math></inline-formula> within the shipping corridor during austral spring and a <inline-formula><mml:math id="M65" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 0.5 W m<inline-formula><mml:math id="M66" 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> IRF<inline-formula><mml:math id="M67" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">ACI</mml:mi></mml:msub></mml:math></inline-formula> in the annual mean. Applying this <inline-formula><mml:math id="M68" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 35 %–70 % decline in IRF<inline-formula><mml:math id="M69" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">ACI</mml:mi></mml:msub></mml:math></inline-formula> to the <inline-formula><mml:math id="M70" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>0.1 to <inline-formula><mml:math id="M71" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>0.6 W m<inline-formula><mml:math id="M72" 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> range of forcing due to shipping emissions from climate models (Capaldo et al., 1999; Lauer et al., 2007; Peters et al., 2013; Righi et al., 2011; Sofiev et al., 2018), global forcing values of <inline-formula><mml:math id="M73" display="inline"><mml:mi>O</mml:mi></mml:math></inline-formula>(0.1 W m<inline-formula><mml:math id="M74" 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>) due to the IMO 2020 regulations are plausible. The strongest shipping effect in Lauer et al. (2007) represented 40 % of their global ACI; a 70 % reduction from that fraction would represent a forcing of <inline-formula><mml:math id="M75" display="inline"><mml:mrow><mml:mn mathvariant="normal">0.2</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">0.1</mml:mn></mml:mrow></mml:math></inline-formula> W m<inline-formula><mml:math id="M76" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mi mathvariant="normal">−</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> based on the currently assessed IRF<inline-formula><mml:math id="M77" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">ACI</mml:mi></mml:msub></mml:math></inline-formula> value of <inline-formula><mml:math id="M78" display="inline"><mml:mrow><mml:mn mathvariant="normal">0.7</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">0.5</mml:mn></mml:mrow></mml:math></inline-formula> W m<inline-formula><mml:math id="M79" 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>, or <inline-formula><mml:math id="M80" display="inline"><mml:mrow><mml:mn mathvariant="normal">0.3</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">0.2</mml:mn></mml:mrow></mml:math></inline-formula> W m<inline-formula><mml:math id="M81" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mi mathvariant="normal">−</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> including adjustments (Forster et al., 2021)</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F5"><?xmltex \currentcnt{5}?><?xmltex \def\figurename{Figure}?><label>Figure 5</label><caption><p id="d1e1054">Probability densities (via Gaussian kernel density estimation) of
IRF<inline-formula><mml:math id="M82" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">ACI</mml:mi></mml:msub></mml:math></inline-formula> for austral spring <bold>(a)</bold> and the annual mean <bold>(b)</bold> over the core
shipping corridor calculated using the changes in <inline-formula><mml:math id="M83" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> (shading) from Eq. (A1) and <inline-formula><mml:math id="M84" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">cld</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> (lines) from Eq. (A2) for the 2002–2019 pre-regulation
climatology (solid light-blue shading and lines) and 2020–2022 post-regulation period (solid dark-gray shading and lines) due to the presence of the shipping corridor and the
2020–2022 minus climatology difference as an estimate of the effect due to
implementation of the IMO 2020 regulations (patterned red shading and lines).</p></caption>
          <?xmltex \igopts{width=241.848425pt}?><graphic xlink:href="https://acp.copernicus.org/articles/23/8259/2023/acp-23-8259-2023-f05.png"/>

        </fig>

</sec>
</sec>
<sec id="Ch1.S4" sec-type="conclusions">
  <label>4</label><title>Conclusions</title>
      <p id="d1e1109">There is a detectable change in large-scale cloud microphysical properties
and evidence supporting a decrease in cloud brightening within the major
southeastern Atlantic shipping corridor after implementation of the IMO 2020
fuel sulfur regulations, resulting in a positive IRF<inline-formula><mml:math id="M85" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">ACI</mml:mi></mml:msub></mml:math></inline-formula> within the
corridor of <inline-formula><mml:math id="M86" display="inline"><mml:mi>O</mml:mi></mml:math></inline-formula>(1 W m<inline-formula><mml:math id="M87" 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>). Although this study did not address potential
changes in cloud adjustments from the IMO 2020 regulations, this will be an
important area of future work, especially<?pagebreak page8264?> as the fuel regulations are
expected not only to decrease overall aerosol numbers but also shift them
toward smaller sizes and sootier composition  (Ault et al., 2010; Lack et
al., 2011; Seppälä et al., 2021).</p>
</sec>

      
      </body>
    <back><app-group>

<app id="App1.Ch1.S1">
  <?xmltex \currentcnt{A}?><label>Appendix A</label><title>Methods</title>
<sec id="App1.Ch1.S1.SS1">
  <label>A1</label><title>Data</title>
      <p id="d1e1159">All cloud, radiation, and meteorological data in this work come from the CERES SSF regional 1<inline-formula><mml:math id="M88" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> <inline-formula><mml:math id="M89" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 1<inline-formula><mml:math id="M90" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> (SSF1deg) monthly product
based on the CERES instrument from the Terra satellite (CERES Science Team, 2021, 2023; Loeb et al., 2018; Wielicki et al., 1996). Radiative fluxes are temporally interpolated over the diurnal cycle assuming constant cloud and meteorological properties but varying the solar zenith angle (Doelling et al., 2013); our results therefore reflect the diurnal average assuming constant Terra conditions rather than the instantaneous midmorning value, which would be much greater in magnitude, but do not account for any diurnal cloud evolution. Overcast albedo values are calculated as in D20 but with the clear-sky albedo assumed to be 0.1 to avoid issues with missing clear-sky data in the SSF1deg product. The
constant clear-sky albedo may cause a high bias in the absolute <inline-formula><mml:math id="M91" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">cld</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> values, especially during the southern African biomass burning season (June to October), but this effect should be small given the very overcast conditions and would not strongly affect the observed versus counterfactual differences. The overcast albedo (albedo as seen from space when clouds are present) differs from the cloud albedo (cloud reflectivity) due to the scattering and absorption of sunlight from above-cloud aerosols and gases.</p>
      <p id="d1e1198">Cloud properties are retrieved from Moderate Resolution Imaging
Spectroradiometer (MODIS) measurements using CERES algorithms (CERES
Science Team, 2016; Minnis et al., 2011), which have some differences from
the standard MODIS products  (Platnick et al., 2017). Only daytime cloud
retrievals utilizing 3.7 <inline-formula><mml:math id="M92" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi></mml:mrow></mml:math></inline-formula>m channel radiances are used in this work.
Low cloud fraction is defined for clouds with cloud-top effective pressure
values greater than 700 hPa.</p>
      <p id="d1e1209">Meteorological variables including surface skin temperature (over oceans,
the Reynold's sea surface temperature), estimated inversion strength
(Wood and Bretherton, 2006), and wind speed are from the NASA Goddard
Space Flight Center Global Modeling and Assimilation Office (GMAO) Goddard
Earth Observing System (GEOS) version 5.4.1  (CERES Science Team,
2021).</p>
      <p id="d1e1212">Sulfur dioxide (SO<inline-formula><mml:math id="M93" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula>) emissions data from 2010 are from the Emissions
Database for Global Atmospheric Research (EDGAR) version 4 (Crippa
et al., 2018) and are identical to those used in D20. The EDGAR SO<inline-formula><mml:math id="M94" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula>
values are only used for identification of the shipping corridor location.</p>
</sec>
<sec id="App1.Ch1.S1.SS2">
  <label>A2</label><title>Shipping corridor identification</title>
      <p id="d1e1241">For each latitude between 8 and 18<inline-formula><mml:math id="M95" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> S,
shipping-affected grid boxes are identified as those with the maximum EDGAR
SO<inline-formula><mml:math id="M96" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula> emission values between 13<inline-formula><mml:math id="M97" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> W and 8<inline-formula><mml:math id="M98" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> E as well
as the four grid boxes to the west and two to the east. This represents a
northward and westward expansion of the shipping corridor definition used in
D20 for their subtropical domain and is intended to better center the
microphysical effects. Ship tracking via the automatic identification system
(AIS) identifies substantial traffic slightly west of where EDGAR places the
maximum SO<inline-formula><mml:math id="M99" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula> emissions, and there are indications of an additional
westward shift in traffic during 2020  (March et
al., 2021). As a sensitivity test, the analysis in Fig. 1 was repeated using
a shipping corridor mask shifted further west by 2<inline-formula><mml:math id="M100" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>, but no notable
differences were found. The core shipping corridor area used in Figs. 3 and
5 and Tables S1–S2 is defined as the central three grid boxes of the shipping
mask for each latitude.</p>
</sec>
<sec id="App1.Ch1.S1.SS3">
  <label>A3</label><title>Universal kriging</title>
      <p id="d1e1307">The universal kriging algorithm mostly follows the implementation of D20,
using the geoR statistical package  (Ribeiro and Diggle, 2018). Universal kriging is a classic geostatistical method  (Zimmerman and Stein, 2010) that has been widely employed in the geosciences and other fields (Chilès and Desassis, 2018), in which estimates of unknown<?pagebreak page8265?> values at some location are informed by nearby observations of the same variable under the assumption that errors around a mean function are spatially correlated as a function of the distance between locations only (stationarity). In our case, counterfactual values for the shipping-affected grid boxes identified above are estimated using the values of nearby non-shipping-affected grid boxes between 8 and 18<inline-formula><mml:math id="M101" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> S and 13<inline-formula><mml:math id="M102" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> W and 8<inline-formula><mml:math id="M103" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> E. Our mean function takes the form of a multiple linear regression model using as regressors some combination of the surface skin temperature (SST), estimated inversion strength (EIS), and wind speed (WS) from the SSF1deg auxiliary data and latitude (lat), longitude (long), and their squares (lat<inline-formula><mml:math id="M104" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:math></inline-formula>, long<inline-formula><mml:math id="M105" display="inline"><mml:mrow><mml:msup><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> and product (lat <inline-formula><mml:math id="M106" display="inline"><mml:mo>⋅</mml:mo></mml:math></inline-formula> long), as determined by whichever combination minimizes the Bayesian information criterion (BIC) to avoid overfitting. Table S1 reports the selected combination of regressors (based on BIC minimization) for each combination of variable (<inline-formula><mml:math id="M107" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M108" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">cld</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> and time period. A logit
transform is applied to the <inline-formula><mml:math id="M109" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">cld</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> values before kriging, which was found by D20 to produce more normally distributed errors around the mean function for bounded fields like albedo and cloud fraction. The stationary error term is then estimated by using weighted least squares to fit a parametric (exponential) covariance model to an empirical variogram (a plot of the squared difference between pairs of variables versus their distance).
Figures S6–S9 show the binned empirical variograms and fitted variograms (see Zimmerman and Stein, 2010) for austral spring <inline-formula><mml:math id="M110" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and logit(<inline-formula><mml:math id="M111" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">cld</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> and annual mean <inline-formula><mml:math id="M112" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and logit(<inline-formula><mml:math id="M113" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">cld</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, respectively. Using the statistical model provided by the kriging process above  (Ribeiro and Diggle, 2018), we simulate 5000 realizations of the NoShip counterfactual for each variable–time-period combination.</p>
</sec>
<sec id="App1.Ch1.S1.SS4">
  <label>A4</label><title>Statistical significance testing</title>
      <p id="d1e1458">Four distinct tests of statistical significance are used in this work, the
first three following D20. Statistical significance for individual
shipping-affected grid boxes is assessed as whether the observed Ship value
exceeds the 97.5th percentile or falls below the 2.5th percentile
of the distribution obtained via kriging for the counterfactual NoShip value
for that grid box.</p>
      <p id="d1e1461">Field significance is assessed by determining whether the number of
individually significant grid boxes calculated above is extreme as compared
to that which could occur by chance under the null hypothesis that the
region is unaffected by shipping; <inline-formula><mml:math id="M114" display="inline"><mml:mi>p</mml:mi></mml:math></inline-formula> values (<inline-formula><mml:math id="M115" display="inline"><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mi mathvariant="normal">field</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) are calculated as
the fraction of the 5000 NoShip simulations that would have a number of
individually significant grid boxes greater than or equal to the factual
case and are adjusted for multiple testing using a Benjamini–Hochberg
adjustment to control the false-discovery rate (Benjamini and Hochberg,
1995; Ventura et al., 2004). When none of the 5000 NoShip simulations
produced a number of individually significant grid boxes as or more extreme
than the Ship field, <inline-formula><mml:math id="M116" display="inline"><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mi mathvariant="normal">field</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is reported as <inline-formula><mml:math id="M117" display="inline"><mml:mi mathvariant="italic">&lt;</mml:mi></mml:math></inline-formula> 0.0001 instead of
zero in Table S1. All <inline-formula><mml:math id="M118" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> perturbations (except 2020–2020 austral
spring) are field significant at a <inline-formula><mml:math id="M119" display="inline"><mml:mi mathvariant="italic">&lt;</mml:mi></mml:math></inline-formula> 0.0001 level; the <inline-formula><mml:math id="M120" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">cld</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>
perturbations have more variation, although all are significant at greater
than 90 % confidence (Fig. 3 and Table S1). Interpreting the field
significance as a measure of the robustness of the shipping effects, we
should therefore have greatest confidence in the <inline-formula><mml:math id="M121" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> results and least
(but still a good deal of) confidence in the annual <inline-formula><mml:math id="M122" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">cld</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> results.</p>
      <p id="d1e1552">The range of Ship–NoShip values generated from the 5000 simulated NoShip
fields is used to assess whether the magnitude of effects within the core
shipping corridor area is statistically distinct from zero at 95 %
confidence (Table S1).</p>
      <p id="d1e1555">Finally, a new test for “detectability” at different confidence interval
thresholds is presented in Table S2 and based on the range of possible
ratios of 2020–2022 over climatological relative Ship–NoShip values from
the 5000 simulated NoShip fields. We adopt significance at 95 %
confidence or greater as distinguishing between “detection” for the
<inline-formula><mml:math id="M123" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> changes versus “evidence” short of detection for the <inline-formula><mml:math id="M124" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">cld</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>
changes.</p>
</sec>
<sec id="App1.Ch1.S1.SS5">
  <label>A5</label><title>Twomey effect calculations</title>
      <p id="d1e1589">For the <inline-formula><mml:math id="M125" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> perturbations, IRF<inline-formula><mml:math id="M126" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">ACI</mml:mi></mml:msub></mml:math></inline-formula> is estimated following Eq. (A1):
            <disp-formula id="App1.Ch1.S1.E1" content-type="numbered"><label>A1</label><mml:math id="M127" display="block"><mml:mrow><?xmltex \hack{\hbox\bgroup\fontsize{9.5}{9.5}\selectfont$\displaystyle}?><mml:msub><mml:mi mathvariant="normal">IRF</mml:mi><mml:mi mathvariant="normal">ACI</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mo>-</mml:mo><mml:msub><mml:mi>F</mml:mi><mml:mo>⊙</mml:mo></mml:msub><mml:msub><mml:mi>C</mml:mi><mml:mi mathvariant="normal">low</mml:mi></mml:msub><mml:msub><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mi mathvariant="normal">atm</mml:mi></mml:msub><mml:msub><mml:mi mathvariant="italic">α</mml:mi><mml:mi mathvariant="normal">cld</mml:mi></mml:msub><mml:mfenced close=")" open="("><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>-</mml:mo><mml:msub><mml:mi mathvariant="italic">α</mml:mi><mml:mi mathvariant="normal">cld</mml:mi></mml:msub></mml:mrow></mml:mfenced><mml:mfenced close=")" open="("><mml:mrow><mml:mo>-</mml:mo><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:msub><mml:mo>/</mml:mo><mml:msub><mml:mi>r</mml:mi><mml:mrow><mml:mi mathvariant="normal">e</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">Ship</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfenced><mml:mo>,</mml:mo><?xmltex \hack{$\egroup}?></mml:mrow></mml:math></disp-formula>
          where <inline-formula><mml:math id="M128" display="inline"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mo>⊙</mml:mo></mml:msub></mml:mrow></mml:math></inline-formula> is the insolation, <inline-formula><mml:math id="M129" display="inline"><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mi mathvariant="normal">low</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the low cloud
fraction, <inline-formula><mml:math id="M130" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mi mathvariant="normal">atm</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is a transfer function between changes in
overcast and cloud albedo (Diamond et al., 2020; Wood, 2021), and <inline-formula><mml:math id="M131" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">α</mml:mi><mml:mi mathvariant="normal">cld</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the cloud albedo. Based on the values in D20, <inline-formula><mml:math id="M132" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mi mathvariant="normal">atm</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is estimated as 0.6 and <inline-formula><mml:math id="M133" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">α</mml:mi><mml:mi mathvariant="normal">cld</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> as 0.5.</p>
      <p id="d1e1752">For the <inline-formula><mml:math id="M134" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">cld</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> perturbations, IRF<inline-formula><mml:math id="M135" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">ACI</mml:mi></mml:msub></mml:math></inline-formula> is estimated following Eq. (A2):
            <disp-formula id="App1.Ch1.S1.E2" content-type="numbered"><label>A2</label><mml:math id="M136" display="block"><mml:mrow><mml:msub><mml:mi mathvariant="normal">IRF</mml:mi><mml:mi mathvariant="normal">ACI</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mo>-</mml:mo><mml:msub><mml:mi>F</mml:mi><mml:mo>⊙</mml:mo></mml:msub><mml:msub><mml:mi>C</mml:mi><mml:mi mathvariant="normal">low</mml:mi></mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">cld</mml:mi></mml:msub><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula>
          Equations (A1) and (A2) neglect liquid water path and cloud fraction adjustments
to the Twomey effect. The effective radiative forcing due to aerosol–cloud
interactions (ERF<inline-formula><mml:math id="M137" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">ACI</mml:mi></mml:msub></mml:math></inline-formula>), accounting for cloud adjustments, would be
greater in magnitude than calculated here if cloudiness were increased via
drizzle suppression and lower if cloudiness were decreased via enhanced
entrainment. D20 found that adjustments were small in the morning but
substantially offset brightening during the afternoon in austral spring. The
apparently small effects in the morning may reflect diurnal competition
between precipitation suppression, which maximizes overnight, and
entrainment drying, which maximizes during the day (Sandu et al.,
2008). Thus, the IRF<inline-formula><mml:math id="M138" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">ACI</mml:mi></mml:msub></mml:math></inline-formula> values here are likely larger than ERF<inline-formula><mml:math id="M139" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">ACI</mml:mi></mml:msub></mml:math></inline-formula>
values would be after accounting for adjustments over the full diurnal
cycle, at least in austral spring.</p><?xmltex \hack{\newpage}?>
</sec>
</app>
  </app-group><notes notes-type="codeavailability"><title>Code availability</title>

      <p id="d1e1843">Code for processing the data and recreating the analyses in this work is available from GitHub (<uri>https://github.com/michael-s-diamond/IMO2020</uri>, last access: 12 June 2023, <ext-link xlink:href="https://doi.org/10.5281/zenodo.8165409" ext-link-type="DOI">10.5281/zenodo.8165409</ext-link>, Diamond, 2023a). The universal kriging algorithm is implemented in R (R Core Team, 2014) using the geoR package (<uri>https://CRAN.R-project.org/package=geoR</uri>, Ribeiro and
Diggle, 2018). Other analyses are performed in Python using the numpy (Harris et al., 2020), cartopy (Met Office, 2010–2015), matplotlib (Hunter, 2007), scipy  (Virtanen et al., 2020), statsmodels (<uri>https://github.com/statsmodels/statsmodels</uri>, statsmodels, 2023) and
xarray (Hoyer and Hamman, 2017) packages.</p>
  </notes><notes notes-type="dataavailability"><title>Data availability</title>

      <p id="d1e1861">SSF1deg data (<ext-link xlink:href="https://doi.org/10.5067/Terra/CERES/SSF1DegMonth_L3.004A" ext-link-type="DOI">10.5067/Terra/CERES/SSF1DegMonth_L3.004A</ext-link>, CERES Science Team, 2023) are available from the NASA Langley Research Center CERES ordering tool
(<uri>https://ceres.larc.nasa.gov/data/</uri>, NASA Langley Research Center, 2023). EDGAR data (European Commission Joint Research Centre, 2018) are available from the European Commission Joint Research Centre Data Catalogue
(<ext-link xlink:href="https://doi.org/10.2904/JRC_DATASET_EDGAR" ext-link-type="DOI">10.2904/JRC_DATASET_EDGAR</ext-link>). Processed data used in this work
are available in a Zenodo repository (<ext-link xlink:href="https://doi.org/10.5281/zenodo.7864530" ext-link-type="DOI">10.5281/zenodo.7864530</ext-link>, Diamond, 2023b).</p>
  </notes><app-group>
        <supplementary-material position="anchor"><p id="d1e1876">The supplement related to this article is available online at: <inline-supplementary-material xlink:href="https://doi.org/10.5194/acp-23-8259-2023-supplement" xlink:title="pdf">https://doi.org/10.5194/acp-23-8259-2023-supplement</inline-supplementary-material>.</p></supplementary-material>
        </app-group><notes notes-type="competinginterests"><title>Competing interests</title>

      <p id="d1e1885">The author has declared that there are no competing interests.</p>
  </notes><notes notes-type="disclaimer"><title>Disclaimer</title>

      <p id="d1e1891">Publisher’s note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.</p>
  </notes><ack><title>Acknowledgements</title><p id="d1e1897">Hannah M. Director merits continued gratitude for her contributions to the
original code base and analysis methods. Discussion with Leon Simons
provided the impetus for attempting to detect a signal with only 3 years
of post-2020 data. Thanks are owed to Clare Singer, Emily de Jong, and an anonymous
reviewer for their constructive comments.</p></ack><notes notes-type="financialsupport"><title>Financial support</title>

      <p id="d1e1902">This research has been supported by the Florida State University (new faculty startup).</p>
  </notes><notes notes-type="reviewstatement"><title>Review statement</title>

      <p id="d1e1908">This paper was edited by Markus Petters and Timothy Garrett  and reviewed by Clare Singer and one anonymous referee.</p>
  </notes><ref-list>
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