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  <front>
    <journal-meta><journal-id journal-id-type="publisher">AMT</journal-id><journal-title-group>
    <journal-title>Atmospheric Measurement Techniques</journal-title>
    <abbrev-journal-title abbrev-type="publisher">AMT</abbrev-journal-title><abbrev-journal-title abbrev-type="nlm-ta">Atmos. Meas. Tech.</abbrev-journal-title>
  </journal-title-group><issn pub-type="epub">1867-8548</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/amt-19-4553-2026</article-id><title-group><article-title>Remote sensing of local-dust across the Canadian Arctic</article-title><alt-title>RS of local-dust across the Canadian Arctic</alt-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author" corresp="yes" rid="aff1">
          <name><surname>Sayedain</surname><given-names>Seyed Ali</given-names></name>
          <email>seyed.ali.sayedain@usherbrooke.ca</email>
        <ext-link>https://orcid.org/0000-0002-2250-0220</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>O'Neill</surname><given-names>Norman T.</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff2">
          <name><surname>Ranjbar</surname><given-names>Keyvan</given-names></name>
          
        <ext-link>https://orcid.org/0000-0002-2328-1963</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff3">
          <name><surname>Gauvin-Bourdon</surname><given-names>Phillipe</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff3">
          <name><surname>Chang</surname><given-names>Rachel</given-names></name>
          
        <ext-link>https://orcid.org/0000-0003-2337-098X</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff4">
          <name><surname>Hayes</surname><given-names>Patrick L.</given-names></name>
          
        <ext-link>https://orcid.org/0000-0002-6985-9601</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff5">
          <name><surname>King</surname><given-names>James</given-names></name>
          
        </contrib>
        <aff id="aff1"><label>1</label><institution>Centre d'Applications et de Recherches en Télédétection, Université de Sherbrooke, Sherbrooke, QC, Canada</institution>
        </aff>
        <aff id="aff2"><label>2</label><institution>Flight Research Laboratory, National Research Council Canada, Ottawa, ON, Canada</institution>
        </aff>
        <aff id="aff3"><label>3</label><institution>Department of Physics and Atmospheric Science, Dalhousie University, Halifax, NS, Canada</institution>
        </aff>
        <aff id="aff4"><label>4</label><institution>Département de chimie, Université de Montréal, Montréal, QC, Canada</institution>
        </aff>
        <aff id="aff5"><label>5</label><institution>Département de géographie, Université de Montréal, Montréal, QC, Canada</institution>
        </aff>
      </contrib-group>
      <author-notes><corresp id="corr1">Seyed Ali Sayedain (seyed.ali.sayedain@usherbrooke.ca)</corresp></author-notes><pub-date><day>10</day><month>July</month><year>2026</year></pub-date>
      
      <volume>19</volume>
      <issue>13</issue>
      <fpage>4553</fpage><lpage>4581</lpage>
      <history>
        <date date-type="received"><day>4</day><month>December</month><year>2025</year></date>
           <date date-type="rev-request"><day>16</day><month>February</month><year>2026</year></date>
           <date date-type="rev-recd"><day>5</day><month>June</month><year>2026</year></date>
           <date date-type="accepted"><day>18</day><month>June</month><year>2026</year></date>
      </history>
      <permissions>
        <copyright-statement>Copyright: © 2026 Seyed Ali Sayedain et al.</copyright-statement>
        <copyright-year>2026</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://amt.copernicus.org/articles/19/4553/2026/amt-19-4553-2026.html">This article is available from https://amt.copernicus.org/articles/19/4553/2026/amt-19-4553-2026.html</self-uri><self-uri xlink:href="https://amt.copernicus.org/articles/19/4553/2026/amt-19-4553-2026.pdf">The full text article is available as a PDF file from https://amt.copernicus.org/articles/19/4553/2026/amt-19-4553-2026.pdf</self-uri>
      <abstract><title>Abstract</title>

      <p id="d2e164">We investigated the optical and microphysical characterization of High- and sub-Arctic dust events across the Canadian Arctic Archipelago (CAA). Events from local sources (local dust) were first identified and characterized using a combination of ground-based lidar, two AERONET instruments, and passive (MODIS, Sentinel-2, MISR) imagery in the neighbourhood of the High-Arctic Polar Environment Atmospheric Research Laboratory (PEARL) at Eureka, Nunavut (on Ellesmere Island in the northernmost part of the CAA).</p>

      <p id="d2e167">The PEARL findings informed the identification and characterization of local dust events over other parts of the CAA using a suite of satellite instruments whose remote sensing (RS) capabilities were complementary to or an extension of the ground- and satellite-based techniques employed at Eureka. The events included plumes emanating from Axel Heiberg Island, just west of Ellesmere Island, Banks Island in the southwest corner of the CAA, Ellef Ringnes Island in the eastern part of the central CAA and Prince of Wales Island/Victoria Island in the central southern CAA. Plume identification, plume source and CM (coarse mode) aerosol optical depth (AOD) retrievals were investigated using a combination of low to high spatial resolution (MODIS to Sentinel-2) color imagery and the MODIS dark target AOD product over water. Plume thickness, height and speed for most of the events were obtained (depending on orbit availability and lack of cloud contamination) from MISR (Multi-angle Imaging Spectro Radiometer) stereoscopic products.</p>

      <p id="d2e170">These RS results support an argument for the ubiquitous presence of pan-Arctic, low altitude dust that is typically (away from any strong sources such as mountainous drainage basins) at the lower levels of detectability offered by ground- and satellite-based RS techniques. The ability to RS airborne, near-source, local dust events and characterize dust properties and dynamics of important regions such as the CAA is critical to understanding local dust impacts such as early snow/ice melt and the nucleation role of local dust in the formation of low-altitude clouds.</p>
  </abstract>
    
<funding-group>
<award-group id="gs1">
<funding-source>Natural Sciences and Engineering Research Council of Canada</funding-source>
<award-id>RGPIN-2023-04943</award-id>
<award-id>RGPIN-2022-03785</award-id>
<award-id>RGPIN-2022-04963</award-id>
</award-group>
<award-group id="gs2">
<funding-source>Canada Research Chairs</funding-source>
<award-id>CRC-2020-00285</award-id>
</award-group>
<award-group id="gs3">
<funding-source>Canadian Space Agency</funding-source>
<award-id>21SUASACOA</award-id>
</award-group>
</funding-group>
</article-meta>
  </front>
<body>
      

<sec id="Ch1.S1" sec-type="intro">
  <label>1</label><title>Introduction</title>
      <p id="d2e182">Local, drainage-flow dust events are recognized as an important source of dust at high latitudes (Bullard et al., 2016) and are a significant contributor to Arctic and sub-Arctic aerosols in terms of total atmospheric (columnar) dust loads and notably, to near-surface concentration and attendant surface deposition (Groot Zwaaftink et al., 2016). Meinander et al. (2022) employed dust-transport simulations supported by recent verification data (including the identification of sources using satellite-based imagery) to confirm the predominance of high-latitude dust (HLD) sources in terms of snow and ice deposition. O'Neill et al. (2025) summarized satellite-derived findings of what was likely local dust deposition (with attendant decreases in visually observed surface reflectance) for a sampling of drainage basin regions in the CAA. Local dust, whose source plumes can produce quite strong coarse mode<fn id="Ch1.Footn1"><p id="d2e185">roughly speaking, particles of super <inline-formula><mml:math id="M1" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula> (radius) size</p></fn> (CM) AODs (aerosol optical depths) eventually spread out and/or are deposited to yield weak, monthly-binned CM AODs (O'Neill et al., 2025 who employ the term DOD [dust optical depths] for the CM AODs known to be dominated by dust).</p>
      <p id="d2e199">Dust from Asian deserts can be transported around the world and contributes to the dust load over the Arctic (see for example Uno et al., 2009). AboEl-Fetouh et al. (2020) argued that there was a small but distinct springtime, pan-Arctic (CM) AOD<fn id="Ch1.Footn2"><p id="d2e202">their CM AODs corresponded to integrations of the retrieved AERONET particle-volume size distribution across retrieval radii ranging from a fixed (interpolated) value of 0.6 <inline-formula><mml:math id="M2" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula> (Dubovik et al., 2002) to an upper bin edge of 17.18 <inline-formula><mml:math id="M3" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula> (AboEl-Fetouh et al., 2020 explicitly define the bin centers and the bid edges in their Table S1)</p></fn> contribution of what was likely Asian dust over six AERONET stations spread across the Canadian and northern European Arctic. They also noted that the particle-volume size distribution (PVSD) associated with those CM AODs showed a peak radius <inline-formula><mml:math id="M4" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 1.3 <inline-formula><mml:math id="M5" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula>. This feature tends to dominate monthly-binned CM AOD averages in the spring (ibid) while DODs associated with local sources are likely more prevalent in the summer and fall according to the monthly-binned simulations (Fig. 7) of Groot Zwaaftink et al. (2016)<fn id="Ch1.Footn3"><p id="d2e243">Their source and receptor regions represent broad “cap” areas that are greater than a certain latitude</p></fn>. Aside from its rather unique temporal signature, Asian dust tends to be concentrated in weak to moderately strong DOD plumes located in the mid- to upper-troposphere with some evidence of dust deposition during the period of relatively strong Asian dust events (see, for example, the Fig. 3 Barrow event of Zhao et al., 2022).</p>
      <p id="d2e247">Local dust particles in the Arctic are known to be strong ice nucleating particles (INPs) that can significantly influence the dynamics of mixed-phase clouds (ice crystals and water droplets) and their optical and radiative impacts (Xi et al., 2022; Kawai et al., 2023). The dust plumes lofted into the atmosphere from the Copper River Delta in southern Alaska during late summer or autumn were, for example, shown to be a major INP source (Barr et al., 2023). Those authors also pointed out that the dust events can last for many days and extend hundreds of kilometers into the Gulf of Alaska. Tobo et al. (2019) noted that the high ice nucleating ability of local dust in the Svalbard region of the European Arctic was likely improved by the presence of organic matter.</p>
      <p id="d2e250">HLD events in the Canadian Arctic and specifically the CAA are rarely monitored and so their properties are, accordingly, not well characterized: low population density and limited numbers of meteorological stations have resulted in a scarcity of observations. Persistent cloudy periods and the attendant underuse of RS data have represented significant challenges to the exploitation of satellite RS data (Bullard et al., 2016). Alternatively, optically thinner clouds and/or surface reflectance perturbations (such as white froth from waves) could act to contaminate AOD retrievals over water.</p>
      <p id="d2e254">Satellite imagery at different spatial and temporal resolutions in the polar regions can provide color images of dust events as well as plume characterization products (including AOD, plume height and thickness, coarse indicators of particle size, etc.) that help to better characterize local dust. Satellite-based, high spatial-resolution RS data can, for example, enable the separation of local dust-plume patterns from suspended sediments and phytoplankton blooms in the water.</p>
      <p id="d2e257">The identification of dust plumes over the Icelandic region using MODIS true color imagery has been reported for events dating back to 2002 (Arnalds, 2010). Satellite- and airborne-RS of local dust over the Arctic (as summarized by Sayedain et al., 2023; SDN) include airborne RS of dust over the riverbed, fjord, and coastal regions of Svalbard, sub-Arctic dust plumes flowing over the Gulf of Alaska (where they are much more readily identified and characterized), and MODIS- and CALIOP-based identification of dust plumes from Iceland. A local, high-Arctic CM dust plume, induced by the drainage basin dynamics of Lake Hazen (<inline-formula><mml:math id="M6" display="inline"><mml:mo lspace="0mm">∼</mml:mo></mml:math></inline-formula> 300 km northeast of Eureka on Ellesmere Island), was identified and characterized by Ranjbar et al. (2021) using various types of passive and active, satellite-based RS tools adapted to the special case of dust optics and microphysics. Baddock et al. (2024) provided a detailed analysis of a dust event over Pearly Land, Northern Greenland employing Sentinel-2 true-color images supported by reanalyzed near-surface wind and temperature data.</p>
      <p id="d2e267">In terms of ground-based RS, Yang et al. (2020) used Doppler lidar (backscatter and depolarization ratio channels) and ceilometer profiles, along with CIMEL photometry (the instrument employed by AERONET) to characterize the optical properties of Icelandic, sub-Arctic dust plumes. Bachelder et al. (2020) reported peak CM radii of <inline-formula><mml:math id="M7" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 1.63 <inline-formula><mml:math id="M8" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula> for their measured near-source particle-mass size distributions (PMSDs) of local dust in the sub-Arctic Ä'äy Chù (Slims River) basin in the Canadian Yukon. SDN characterized the optical and microphysical properties of Lhù'ààn Mân'<fn id="Ch1.Footn4"><p id="d2e287">The Kluane Lake Research Station about 8 km east of the Ä'äy Chù measurement station</p></fn> dust plumes using CIMEL and Doppler lidar instrumentation supported by microphysical surface measurements. Their CIMEL- and lidar-derived dust AODs (which we will refer to as DODs in cases where dust is likely the predominant aerosol) were CM dominated (weaker fine mode DODs that correlated with the CM DODs were also observed).</p>
      <p id="d2e291">Kawai et al. (2023) simulated the columnar mass concentrations of local dust in the Arctic in order to lay the groundwork for their investigations into the strong role of local dust as INP. They employed CALIOP profiles and the CALIOP aerosol subtype classification product to produce a local-dust Arctic DOD climatology in order to verify the quality of their dust simulations. Their map of simulated columnar mass abundance of pan-Arctic dust helped contextualize (roughly guide or even semi-quantitatively validate) our search for dust events in the CAA that would be detectable using satellite-based RS. In general, we expect DODs associated with local dust to be dominated by CM particles (see, for example, the overview given in O'Neill et al., 2025).</p>
      <p id="d2e294">The instruments and measurements that we employed in the investigations reported in this paper, reflect a general strategy of using ground-based microphysical as well as ground-based passive and active RS measurements acquired at the High-Arctic PEARL observatory as a means of demonstrating the presence of local dust in the PEARL region and then linking, by direct or indirect means, this information with imagery available from the very frequent overpasses of satellite-based instruments over a site that is near the tangent circle of all polar-orbiting satellites (and thus the beneficiary of a high density of RS data). With this type of analysis in hand we sought to support/inform (without the ground-based RS and microphysical sampling capabilities of the PEARL complex), the purely satellite-based RS and characterization of local dust events in other parts of the CAA. The motivation for this work was to analyze and help verify/evaluate elements of the large potential trove of satellite-based dust RS data over the CAA.</p>
</sec>
<sec id="Ch1.S2">
  <label>2</label><title>Study Area</title>
<sec id="Ch1.S2.SS1">
  <label>2.1</label><title>The Canadian Arctic Archipelago</title>
      <p id="d2e312">The CAA extends from the northern (low Arctic) shores of the Canadian mainland to the high Arctic (Fig. 1a). It consists of a group of approximately 36 000 islands, many of which are covered by ice for much of the year (Adams et al., 2015). Different local CAA dust events at Eureka on Ellesmere Island, Axel Heiberg Island, Prince of Wales Island, Banks Island, and Ellef Ringnes Island were investigated as part of this local dust analysis.</p>

      <fig id="F1" specific-use="star"><label>Figure 1</label><caption><p id="d2e317"><bold>(a)</bold> The geographical extent of the CAA as indicated by light-blue shading. The PEARL observatory at Eureka, Nunavut is indicated by a yellow star, <bold>(b)</bold> the PEARL complex showing both the 0PAL (left) and Ridge lab (right) sites (a wide-angle photo of the PEARL complex is below those photos). The nominal (AERONET) coordinates of the 0PAL and Ridge lab sites are, respectively; 79.990° N, 85.939° W at 5 m elevation and 80.054° N, 86.417° W at 615 m elevation.</p></caption>
          <graphic xlink:href="https://amt.copernicus.org/articles/19/4553/2026/amt-19-4553-2026-f01.png"/>

        </fig>

<sec id="Ch1.S2.SS1.SSSx1" specific-use="unnumbered">
  <title>The PEARL research complex</title>
      <p id="d2e336">The Polar Environment Atmospheric Research Laboratory (PEARL) at Eureka is an important High-Arctic location where optical and microphysical measurements of gases, aerosols and clouds are conducted on a quasi-continuous basis. The PEARL complex (indicated by a star on the map of Fig. 1a) includes two atmospheric measurement sites (Fig. 1b): the 0PAL (Zero Altitude PEARL Auxiliary Laboratory) at 5 m a.s.l., and the Ridge lab at 615 m a.s.l. The 0PAL site and the Ridge lab are separated by a 15 km-long gravel road.</p>
</sec>
</sec>
</sec>
<sec id="Ch1.S3">
  <label>3</label><title>Instrumentation and Methodology</title>
      <p id="d2e350">In this section, we present a brief overview of the instruments and measurements employed in our local dust investigations at the PEARL complex and a summary of the satellite imagery products that we employed over targeted CAA sites in our search for detectable dust events.</p>
<sec id="Ch1.S3.SS1">
  <label>3.1</label><title>Sun photometer/sky radiometer</title>
      <p id="d2e360">Spectral AOD and almucantar sky radiance measurements were acquired by two automated AERONET CIMEL sun photometer/sky radiometers (see Giles et al., 2019, for recent details on the CIMEL instrument and the AERONET  network). The Canadian sub-network of AERONET (AEROCAN) is run by Environment and Climate Change Canada (ECCC) in collaboration with AERONET (Ihab Abboud is the AEROCAN coordinator). The Ridge lab and the 0PAL CIMEL have been in operation from 2007 to 2019 and from 2007 to the present, respectively<fn id="Ch1.Footn5"><p id="d2e363">The AERONET database name for “0PAL” is written as “OPAL”</p></fn>. The Ridge lab CIMEL is labeled ”PEARL” in the AERONET database.</p>
      <p id="d2e367">The CIMEL instruments acquire solar-disk irradiances across eight spectral channels from the ultraviolet (UV) to the short-wave infrared (SWIR) at central wavelengths (<inline-formula><mml:math id="M9" display="inline"><mml:mi mathvariant="italic">λ</mml:mi></mml:math></inline-formula>) of 340, 380, 440, 500, 675, 870, 1020, and 1640 nm in a sequence of three 10 s (triplet) observation at a nominal temporal resolution of 3 min between triplets (15 min for older CIMEL versions). Version 3, Level 1.0 AERONET AODs were employed in the analysis (unless otherwise stated). These AOD spectra yield fine mode (FM) and coarse mode (CM) AODs (the AERONET SDA product at 500 nm wavelength) with pre-cloud-screened filtering being driven by a ceiling on the variation of the triplets (see Giles et al., 2019, for AERONET processing details and products).</p>
      <p id="d2e377">The CIMELs also acquire (low frequency) AOD spectra and almucantar radiances across four spectral bands (380, 440, 675, 870 nm) at a nominal temporal resolution of 1 h<fn id="Ch1.Footn6"><p id="d2e380">supplemented by 4 additional AOD/almucantar measurement series at solar airmasses of 4, 3, 2 and 1.7 (Sinyuk et al., 2020).</p></fn>. Version 3, Level 1.5 (cloud-screened) AOD measurements and associated almucantar radiances are inverted to yield (what amount to) columnar averages of refractive index and PVSDs.</p>
</sec>
<sec id="Ch1.S3.SS2">
  <label>3.2</label><title>Aerodynamic Particle Sizer Spectrometer</title>
      <p id="d2e392">The Aerodynamic Particle Sizer (APS) spectrometer measures both aerodynamic diameter and light-scattering intensity (TSI Incorporated, 2022). Their basic size distribution product is a largely CM product (52 optical channels with an aerodynamic particle diameter range between 0.5 and 20 <inline-formula><mml:math id="M10" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula>). The chosen temporal bin-sampling frequency was 1 min. Particle-number size distributions (<inline-formula><mml:math id="M11" display="inline"><mml:mrow><mml:mi mathvariant="normal">d</mml:mi><mml:mi>N</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">d</mml:mi><mml:mi>log⁡</mml:mi><mml:mi>D</mml:mi></mml:mrow></mml:math></inline-formula>) are calculated by dividing the measured number concentration of each bin by its logarithmic bin size (<inline-formula><mml:math id="M12" display="inline"><mml:mrow><mml:mi mathvariant="normal">d</mml:mi><mml:mi>log⁡</mml:mi><mml:mi>D</mml:mi></mml:mrow></mml:math></inline-formula>). PVSD concentrations (<inline-formula><mml:math id="M13" display="inline"><mml:mrow><mml:mi mathvariant="normal">d</mml:mi><mml:mi>v</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">d</mml:mi><mml:mi>log⁡</mml:mi><mml:mi>D</mml:mi></mml:mrow></mml:math></inline-formula>) are then expressed in terms of equivalent spherical particles (<inline-formula><mml:math id="M14" display="inline"><mml:mrow><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mn mathvariant="normal">4</mml:mn><mml:mn mathvariant="normal">3</mml:mn></mml:mfrac></mml:mstyle><mml:mi mathvariant="italic">π</mml:mi><mml:mo>(</mml:mo><mml:mi>D</mml:mi><mml:mo>/</mml:mo><mml:mn mathvariant="normal">2</mml:mn><mml:msup><mml:mo>)</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:msup><mml:mi mathvariant="normal">d</mml:mi><mml:mi>N</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">d</mml:mi><mml:mi>log⁡</mml:mi><mml:mi>D</mml:mi></mml:mrow></mml:math></inline-formula>). CM particle-volume concentrations (<inline-formula><mml:math id="M15" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi>c</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> are obtained by adding the <inline-formula><mml:math id="M16" display="inline"><mml:mrow><mml:mi mathvariant="normal">d</mml:mi><mml:mi>v</mml:mi></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M17" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> PVSDs <inline-formula><mml:math id="M18" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M19" display="inline"><mml:mrow><mml:mi mathvariant="normal">d</mml:mi><mml:mi>log⁡</mml:mi><mml:mi>D</mml:mi></mml:mrow></mml:math></inline-formula> across a range of CM channels<fn id="Ch1.Footn7"><p id="d2e543">from bin (<inline-formula><mml:math id="M20" display="inline"><mml:mi>i</mml:mi></mml:math></inline-formula>) <inline-formula><mml:math id="M21" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 21 to 52. This bin range corresponds to geometric bin center diameters of <inline-formula><mml:math id="M22" display="inline"><mml:mi>D</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M23" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 1.47 to 13.66 <inline-formula><mml:math id="M24" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula>. Geometric diameters are taken as the aerodynamic diameter<inline-formula><mml:math id="M25" display="inline"><mml:mo>/</mml:mo></mml:math></inline-formula>1.45 (see, for example, Huang et al., 2021).</p></fn> (<inline-formula><mml:math id="M26" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi>c</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M27" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M28" display="inline"><mml:mrow><mml:msubsup><mml:mo>∑</mml:mo><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">21</mml:mn></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">52</mml:mn></mml:mrow></mml:msubsup><mml:mi mathvariant="normal">d</mml:mi><mml:mi>v</mml:mi></mml:mrow></mml:math></inline-formula>).</p>
</sec>
<sec id="Ch1.S3.SS3">
  <label>3.3</label><title>Arctic High Spectral Resolution Lidar</title>
      <p id="d2e647">The Arctic High Spectral Resolution Lidar (AHSRL) was deployed at 0PAL between August 2005 and June 2010. The AHSRL employs Doppler-type lidar technology to separate (slow-moving aerosol and fast-moving molecular), velocity-induced differences in Doppler frequencies. This separation enables the retrieval of particle (aerosol and/or cloud) to molecular backscatter coefficient ratios that, in turn, allow for the extraction of particle backscatter profiles by the simple expediency of multiplying by the relatively well-known molecular backscattering profile (see Eloranta's HSRL chapter in Weitkamp, 2005). The AHSRL provides backscatter coefficient<fn id="Ch1.Footn8"><p id="d2e650">What the lidar community refers to as backscatter cross section (but which we have adapted to better fit into the extinction coefficient vocabulary of the radiative transfer community; see, for example, Hansen and Travis, 1974)</p></fn> (<inline-formula><mml:math id="M29" display="inline"><mml:mi mathvariant="italic">β</mml:mi></mml:math></inline-formula> with units of sr<sup>−1</sup> km<sup>−1</sup>) and volume depolarization ratio (VDR<fn id="Ch1.Footn9"><p id="d2e685">For purposes of symbolic brevity, we also employ <inline-formula><mml:math id="M32" display="inline"><mml:mi mathvariant="italic">δ</mml:mi></mml:math></inline-formula> to represent VDR in any equation context.</p></fn>) profiles of 7.5 m vertical resolution up to 30 km of altitude and inter-sample resolution of 1 min (Eloranta et al., 2004). The VDR is a well-known source of information related to the optical separation of FM and CM contributions to the backscatter signal. We employ that type of information below to make links with CM AODs (DODs) derived from the CIMEL instruments.</p>
      <p id="d2e696">The <inline-formula><mml:math id="M33" display="inline"><mml:mi mathvariant="italic">β</mml:mi></mml:math></inline-formula> altitude profiles can be integrated to yield what we refer to as the particulate backscatter optical depth (<inline-formula><mml:math id="M34" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mi mathvariant="italic">β</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> whose FM and CM AOD components are <inline-formula><mml:math id="M35" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow><mml:mi mathvariant="italic">β</mml:mi><mml:mo>,</mml:mo><mml:mi>f</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M36" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow><mml:mi mathvariant="italic">β</mml:mi><mml:mo>,</mml:mo><mml:mi>c</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>. If the FM and CM profiles are largely dominated by homogeneous particle types (like, respectively, FM sulphatic-based pollution particles and CM dust) then their corresponding optical depths are given by <inline-formula><mml:math id="M37" display="inline"><mml:mrow><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mi>f</mml:mi><mml:mi>l</mml:mi></mml:msubsup></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M38" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M39" display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi>f</mml:mi></mml:msub><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow><mml:mi mathvariant="italic">β</mml:mi><mml:mo>,</mml:mo><mml:mi>f</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M40" display="inline"><mml:mrow><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mi>c</mml:mi><mml:mi>l</mml:mi></mml:msubsup></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M41" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M42" display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi>c</mml:mi></mml:msub><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow><mml:mi mathvariant="italic">β</mml:mi><mml:mo>,</mml:mo><mml:mi>c</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> (where <inline-formula><mml:math id="M43" display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi>f</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M44" display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi>c</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> are the lidar ratios [sr] of the FM and CM particle types).</p>
</sec>
<sec id="Ch1.S3.SS4">
  <label>3.4</label><title>Satellite imagery</title>
      <p id="d2e866">MODIS satellite images along with their derived AOD products as well as MISR multi-view images and their AOD, plume height and plume speed products were employed to investigate a variety of dust events using the contextualizing diversity of information layers available from the NASA Worldview<fn id="Ch1.Footn10"><p id="d2e869"><uri>https://worldview.earthdata.nasa.gov/</uri> (last access: 2 December 2025)</p></fn> application. High spatial resolution Sentinel-2 color images from the Copernicus Browser<fn id="Ch1.Footn11"><p id="d2e875"><uri>https://dataspace.copernicus.eu/browser</uri> (last access:  2 December 2025)</p></fn> were also employed on an as-needed basis: they often yielded physical and/or spatio-temporal insights into local dust behavior that was not obvious in the (comparatively) low-resolution MODIS imagery and products.</p>
<sec id="Ch1.S3.SS4.SSS1">
  <label>3.4.1</label><title>MODIS</title>
      <p id="d2e888">MODIS multispectral imagers operate on both the descending-orbit (Terra) and ascending orbit (Aqua) satellites at an altitude of 705 km<fn id="Ch1.Footn12"><p id="d2e891">Local-time equatorial crossings of 10:30 and 13:30, respectively</p></fn>. MODIS employs 36 spectral bands between 400 nm (UV) and 14.4 <inline-formula><mml:math id="M45" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula> (thermal-IR) at three different nadir spatial resolutions of 250 m (bands 1–2), 500 m (bands 3–7), and 1 km (bands 8–36). The sensor has a swath width of 2330 km (cross-track) by 10 km (along track at nadir) and views the entire Earth every 1 to 2 d, depending on the latitude of the orbit line (Justice et al., 2002). The MODIS “true color” RGB images provided by the NASA Worldview application have a spatial resolution of 250 m (R <inline-formula><mml:math id="M46" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> Band 1 at 620–670 nm, G <inline-formula><mml:math id="M47" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> Band 4 at 545–565 nm, B <inline-formula><mml:math id="M48" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> Band 3 at 459–479 nm).</p>
      <p id="d2e926">The highest-resolution, 3 km land and ocean (550 nm) AOD products (Terra, MOD04_3K, and Aqua, MYD04_3K) are computed using the Dark Target (DT) algorithms over dark land and ocean targets during daytime overpasses (Levy et al., 2015a, b). We employed the 3 km data while monitoring the predictions of the 10 km Deep Blue (DB) AOD product over Arctic land surfaces (Levy et al., 2015c, d) where the DT AOD product was typically sparse or non-existent. The DT algorithm's dependence on the presence of dense dark vegetation to achieve its dark pixel threshold over land is rarely achieved over the Arctic: the DB algorithm was designed to retrieve AOD over surfaces such as deserts or arid lands that are bright in the visible wavelength spectrum (Sayer et al., 2014). It is tempting to employ this product given that vegetation-sparse Arctic tundra often satisfies the conditions for the generation of DB AODs. However, it is a largely untested product over high-Arctic sites (Andrew Sayer, personal communication, 2025) and our investigations showed the presence of frequent AOD plumes (patches) that were often inordinately coincident with persistently dark reflectance patterns in the imagery. In the end we relied almost exclusively on the DT retrieval over water surfaces.</p>
      <p id="d2e929">We employed the MODIS FMF (Fine Mode Fraction) product (Song et al., 2021) as a means of separating out the CM AOD from the AOD (CM AOD <inline-formula><mml:math id="M49" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> (1 <inline-formula><mml:math id="M50" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula> FMF) <inline-formula><mml:math id="M51" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> AOD). As indicated above, the DOD is generally expected to be dominated by CM particles. Sea-spray particles are also CM in nature: however, the unique spatial nature of dust plumes and their land-based origin largely occluded any possible mixup with sea-salt particles.</p>
</sec>
<sec id="Ch1.S3.SS4.SSS2">
  <label>3.4.2</label><title>MISR</title>
      <p id="d2e961">The Multi-angle Imaging SpectroRadiometer (MISR), aboard the Terra satellite, acquires images of the same scene at nine different viewing angles. The imagery ranges from aft- or backward-looking (<inline-formula><mml:math id="M52" display="inline"><mml:mo lspace="0mm">-</mml:mo></mml:math></inline-formula>70°) to fore- or forward-looking (<inline-formula><mml:math id="M53" display="inline"><mml:mo lspace="0mm">+</mml:mo></mml:math></inline-formula>70°) views in four spectral bands (blue at 447 nm, green at 558 nm, red at 672 nm, and near-infrared at 867 nm). The “Global Mode” nadir spatial resolution is 275 m which degrades to 1.1 km for all off-nadir bands except the red band (MISR Handbook, 2000). The latitude-dependent revisit time is every 2 to 9 d across a 380 km swath (Garay et al., 2020). The stereoscopic nature of the 9 MISR images enables the extraction of plume height and plume velocity. Both parameters are critical for dust plume investigations. This was notably, demonstrated by Ranjbar et al. (2021), for the case of a strong local-dust plume over Lake Hazen (about 330 km northeast of PEARL) that was characterized using MISR, MODIS, CALIOP and CloudSat data. More detailed information on MISR stereoscopic height and wind speed retrievals and the algorithm used to generate these products (the MISR INteractive eXplorer or MINX algorithm) can be found in Nelson et al. (2013), who also provide case studies of plume height and wind speed retrievals for smoke, dust, and cloud.</p>
      <p id="d2e978">It was known, from its earliest conception, that the multi-angle feature of MISR would facilitate the extraction of aerosol parameters given their spatial invariance relative to the typically high frequency spatial variance and differing spectra of surface reflectance (see, for example, the definitive overview of Martonchik et al., 1998). The specific stereoscopic capabilities of MISR enable, in turn, the detection of aerosol or cloud plumes and the computation of their optical depth (see, for example, Kahn et al., 2007, for the case of dust, smoke and volcanic plumes at the 17.6 km atmospheric processing resolution). More recent versions of the MISR processing chain included a 4.4 km resolution, near real time, V23, Level 2 AOD product (Witek et al., 2021) whose AODs are reported at the standard reference wavelength of 550 nm (ibid). We employed both the MISR plume height and AOD products in our investigations of local-dust events across the CAA.</p>
</sec>
</sec>
</sec>
<sec id="Ch1.S4">
  <label>4</label><title>Results and Discussion</title>
      <p id="d2e992">Our results are reported in two subsections: 4.1 – “Analysis of dust events at Eureka” and 4.2 – “Satellite-based RS of local dust events across the CAA”. Our goal is to demonstrate how an experienced-based local dust narrative can be built using the ground-based optical and microphysical measurements of dust plumes in the Eureka region while underscoring what can be achieved using satellite-based RS data that is informed, as much as possible, by the ground-based and satellite-based results at Eureka.</p>
<sec id="Ch1.S4.SS1">
  <label>4.1</label><title>Analysis of dust events at Eureka</title>
      <p id="d2e1002">We carried out a purely optical analysis comparing CIMEL and AHSRL data<fn id="Ch1.Footn13"><p id="d2e1005">over the extended period that the two data sets were mutually available (August 2005 to June 2010)</p></fn> in order to investigate certain optical dynamics that were consistent with the apparent presence of dust particles at low elevations between 0PAL and the Ridge lab. In a different sequence of aerosol events, the 0PAL CIMEL AOD measurements and in situ APS PVSDs shared a common measurement period from 9 July to 20 September 2018. These two periods were an important focus of our ground-based analysis at the PEARL sites. The correlation between different independent datasets was a key aspect of a multi-pronged strategy to provide evidence of Arctic dust events whose RS detectability can be generally characterized as weak to marginal (O'Neill et al., 2025).</p>
<sec id="Ch1.S4.SS1.SSS1">
  <label>4.1.1</label><title>Passive vs. active (ground-based) optical analysis at Eureka</title>
      <p id="d2e1016">Potential dust events over the August 2005 to June 2010 period (the duration of AHSRL measurements at 0PAL) were investigated by looking for low-altitude, large-amplitude VDR events whose derived CM AODs were correlated with the 0PAL CM AOD (<inline-formula><mml:math id="M54" display="inline"><mml:mrow><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mi>c</mml:mi><mml:mi mathvariant="normal">O</mml:mi></mml:msubsup></mml:mrow></mml:math></inline-formula>) and not correlated with the PEARL CM AOD (<inline-formula><mml:math id="M55" display="inline"><mml:mrow><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mi>c</mml:mi><mml:mi mathvariant="normal">P</mml:mi></mml:msubsup></mml:mrow></mml:math></inline-formula>) (if the plumes were found to be largely below the PEARL_CIMEL elevation of 615 m). The AHSRL CM AODs (<inline-formula><mml:math id="M56" display="inline"><mml:mrow><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mi>c</mml:mi><mml:mi>l</mml:mi></mml:msubsup></mml:mrow></mml:math></inline-formula>) were obtained by integrating CM lidar backscatter coefficient (<inline-formula><mml:math id="M57" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">β</mml:mi><mml:mi>c</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) profiles associated with VDR values greater than a particular threshold (<inline-formula><mml:math id="M58" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">δ</mml:mi><mml:mi mathvariant="normal">thr</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) (from the 0PAL to Ridge lab elevations) and employing prescribed FM and CM lidar ratios. The reader is directed to Appendix A1 for a discussion of the FM/CM attributions between the 0PAL and PEARL CIMELs and for temporal resampling details (the resampling of <inline-formula><mml:math id="M59" display="inline"><mml:mrow><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mi>c</mml:mi><mml:mi mathvariant="normal">P</mml:mi></mml:msubsup></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M60" display="inline"><mml:mrow><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mi>c</mml:mi><mml:mi>l</mml:mi></mml:msubsup></mml:mrow></mml:math></inline-formula> measurements to <inline-formula><mml:math id="M61" display="inline"><mml:mrow><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mi>c</mml:mi><mml:mi mathvariant="normal">O</mml:mi></mml:msubsup></mml:mrow></mml:math></inline-formula> times). The theoretical VDR-driven FM/CM attributions for the lidar are defined in Appendix A2.</p>
      <p id="d2e1120">We analyzed the AHSRL profile statistics of 7 events that we claimed to be dust events in Sect. A3.2. The impact of varying the FM/CM attribution threshold of the VDRs (the value of <inline-formula><mml:math id="M62" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">δ</mml:mi><mml:mi mathvariant="normal">thr</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) is detailed in Appendix A3.3<fn id="Ch1.Footn14"><p id="d2e1134">Appendix A3.1 is a discussion of how we filtered (weighted) out severe outliers that could appear in the VDR profiles</p></fn>. We eventually determined that a 5 % VDR threshold for separating CM and FM optical depths was a reasonable compromise. The AHSRL profile details as well as the corresponding derived values of <inline-formula><mml:math id="M63" display="inline"><mml:mrow><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mi>c</mml:mi><mml:mi>l</mml:mi></mml:msubsup></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M64" display="inline"><mml:mrow><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mi>c</mml:mi><mml:mi mathvariant="normal">O</mml:mi></mml:msubsup></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M65" display="inline"><mml:mrow><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mi>c</mml:mi><mml:mi mathvariant="normal">P</mml:mi></mml:msubsup></mml:mrow></mml:math></inline-formula>, and the 0PAL minus PEARL difference (<inline-formula><mml:math id="M66" display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mi>c</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) are shown in Figs. S1a to S7a<fn id="Ch1.Footn15"><p id="d2e1191">Supplementary PowerPoint file “AHSRL_CIMEL_event_profiles”</p></fn> while the summary (profile- and event-integrated) VDR statistics for those lidar profiles are given in Figs. S1b to S7b of the same file (with the overarching VDR statistics being given in the table of Fig. S8). A brief overview of those overarching statistics is given in Sect. A3.2.</p>
      <p id="d2e1195">Figure 2 shows the calculated cloud-screened CM AODs during the apparent dust event of 23 July 2007 (what we call Event 5). We chose it to illustrate the key elements in support of our dust plume detection claims. The <inline-formula><mml:math id="M67" display="inline"><mml:mrow><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mi>c</mml:mi><mml:mi>l</mml:mi></mml:msubsup></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M68" display="inline"><mml:mrow><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow><mml:mi>c</mml:mi><mml:mo>,</mml:mo><mml:mn mathvariant="normal">1.5</mml:mn></mml:mrow><mml:mi mathvariant="normal">O</mml:mi></mml:msubsup></mml:mrow></mml:math></inline-formula> values show the high frequency variations that we argue are due to near surface dust. The (high frequency) similarities between the <inline-formula><mml:math id="M69" display="inline"><mml:mrow><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mi>c</mml:mi><mml:mi>l</mml:mi></mml:msubsup></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M70" display="inline"><mml:mrow><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow><mml:mi>c</mml:mi><mml:mo>,</mml:mo><mml:mn mathvariant="normal">1.5</mml:mn></mml:mrow><mml:mi mathvariant="normal">O</mml:mi></mml:msubsup></mml:mrow></mml:math></inline-formula> “spikes” (coupled with the low frequency unresponsiveness of <inline-formula><mml:math id="M71" display="inline"><mml:mrow><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow><mml:mi>c</mml:mi><mml:mo>,</mml:mo><mml:mn mathvariant="normal">1.5</mml:mn></mml:mrow><mml:mi mathvariant="bold">P</mml:mi></mml:msubsup></mml:mrow></mml:math></inline-formula> to those spikes) are coherent with an argument for the presence of a weak, low-altitude dust event. The standard deviation (SD) of <inline-formula><mml:math id="M72" display="inline"><mml:mrow><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow><mml:mi>c</mml:mi><mml:mo>,</mml:mo><mml:mn mathvariant="normal">1.5</mml:mn></mml:mrow><mml:mi mathvariant="normal">O</mml:mi></mml:msubsup></mml:mrow></mml:math></inline-formula> is generally significantly larger than the SD of <inline-formula><mml:math id="M73" display="inline"><mml:mrow><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow><mml:mi>c</mml:mi><mml:mo>,</mml:mo><mml:mn mathvariant="normal">1.5</mml:mn></mml:mrow><mml:mi mathvariant="normal">P</mml:mi></mml:msubsup></mml:mrow></mml:math></inline-formula> (this disparity amounts to a quantitative verification of the relative unresponsiveness of <inline-formula><mml:math id="M74" display="inline"><mml:mrow><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow><mml:mi>c</mml:mi><mml:mo>,</mml:mo><mml:mn mathvariant="normal">1.5</mml:mn></mml:mrow><mml:mi mathvariant="normal">P</mml:mi></mml:msubsup></mml:mrow></mml:math></inline-formula>).</p>

      <fig id="F2" specific-use="star"><label>Figure 2</label><caption><p id="d2e1336">Level 1.5 (cloud-screened) CM AOD time series of the 23 July 2007 dust event (Event 5 of our 7 dust events) for the CIMELs at 0PAL (<inline-formula><mml:math id="M75" display="inline"><mml:mrow><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow><mml:mi>c</mml:mi><mml:mo>,</mml:mo><mml:mn mathvariant="normal">1.5</mml:mn></mml:mrow><mml:mi mathvariant="normal">O</mml:mi></mml:msubsup></mml:mrow></mml:math></inline-formula>) and PEARL (<inline-formula><mml:math id="M76" display="inline"><mml:mrow><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow><mml:mi>c</mml:mi><mml:mo>,</mml:mo><mml:mn mathvariant="normal">1.5</mml:mn></mml:mrow><mml:mi mathvariant="normal">P</mml:mi></mml:msubsup></mml:mrow></mml:math></inline-formula>) as well as the 0PAL AHSRL (<inline-formula><mml:math id="M77" display="inline"><mml:mrow><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mi>c</mml:mi><mml:mi>l</mml:mi></mml:msubsup></mml:mrow></mml:math></inline-formula>) (altitude range of 5 to 615 m). The <inline-formula><mml:math id="M78" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">δ</mml:mi><mml:mi mathvariant="normal">thr</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> value for separating CM and FM AODs was 5 %. <inline-formula><mml:math id="M79" display="inline"><mml:mrow><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow><mml:mi>c</mml:mi><mml:mo>,</mml:mo><mml:mn mathvariant="normal">1.5</mml:mn></mml:mrow><mml:mi mathvariant="normal">O</mml:mi></mml:msubsup></mml:mrow></mml:math></inline-formula> should, normally, be greater than <inline-formula><mml:math id="M80" display="inline"><mml:mrow><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow><mml:mi>c</mml:mi><mml:mo>,</mml:mo><mml:mn mathvariant="normal">1.5</mml:mn></mml:mrow><mml:mi mathvariant="normal">P</mml:mi></mml:msubsup></mml:mrow></mml:math></inline-formula> but the nominal CIMEL accuracy of <inline-formula><mml:math id="M81" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 0.01/airmass (for both the 0PAL and PEARL CIMELs) is a key factor in the absolute comparison of these very small CM AOD values. The solid, blue-toned bands show the running standard deviation (SD) about the running mean over 30 min intervals with the first-interval mid-point starting at 10:15 UTC (we produced these bands to focus on the high frequency differences between <inline-formula><mml:math id="M82" display="inline"><mml:mrow><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow><mml:mi>c</mml:mi><mml:mo>,</mml:mo><mml:mn mathvariant="normal">1.5</mml:mn></mml:mrow><mml:mi mathvariant="normal">O</mml:mi></mml:msubsup></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M83" display="inline"><mml:mrow><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow><mml:mi>c</mml:mi><mml:mo>,</mml:mo><mml:mn mathvariant="normal">1.5</mml:mn></mml:mrow><mml:mi mathvariant="normal">P</mml:mi></mml:msubsup></mml:mrow></mml:math></inline-formula> (to avoid the standard deviation contributions of more low frequency variations)).</p></caption>
            <graphic xlink:href="https://amt.copernicus.org/articles/19/4553/2026/amt-19-4553-2026-f02.png"/>

          </fig>

      <p id="d2e1485">The <inline-formula><mml:math id="M84" display="inline"><mml:mrow><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mi>c</mml:mi><mml:mi>l</mml:mi></mml:msubsup></mml:mrow></mml:math></inline-formula> vs. <inline-formula><mml:math id="M85" display="inline"><mml:mrow><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow><mml:mi>c</mml:mi><mml:mo>,</mml:mo><mml:mn mathvariant="normal">1.5</mml:mn></mml:mrow><mml:mi mathvariant="normal">O</mml:mi></mml:msubsup></mml:mrow></mml:math></inline-formula> intra-event statistics show marginal to moderately large correlation coefficients (<inline-formula><mml:math id="M86" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula> values from 0.41 to 0.64) for each of the seven events while the inter-event correlation coefficient for the ensemble of seven events was significant (<inline-formula><mml:math id="M87" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M88" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 0.78). The complete ensemble of individual CM AOD measurements in August and July 2007 show diurnal examples of what we determined to be largely dust-free conditions in the 0PAL to PEARL layer. A particular example on 19 July 2007, occurred in the presence of very clear background columnar conditions above the 0PAL and PEARL CIMELs<fn id="Ch1.Footn16"><p id="d2e1541">Across that layer we found <inline-formula><mml:math id="M89" display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mi>c</mml:mi><mml:mi>l</mml:mi></mml:msubsup></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M90" display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mi>c</mml:mi><mml:mi mathvariant="normal">O</mml:mi></mml:msubsup></mml:mrow></mml:math></inline-formula> to be quite small (<inline-formula><mml:math id="M91" display="inline"><mml:mo lspace="0mm">&lt;</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M92" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 0.0003) and <inline-formula><mml:math id="M93" display="inline"><mml:mo>&lt;</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M94" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 0.0002 respectively).</p></fn>: it was thus an explicit example of clean background conditions that could be used as reference for declarations of time-varying dust events in the layer between the two events.</p>
</sec>
<sec id="Ch1.S4.SS1.SSS2">
  <label>4.1.2</label><title>Optical vs microphysical (ground-based) analysis at Eureka</title>
      <p id="d2e1612">Figure 3 encapsulates the analysis that we carried out in the comparison of the CIMEL CM AODs and APS <inline-formula><mml:math id="M95" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi>c</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> values associated with an event that we argue was a significant dust event at Eureka. The simultaneous rise of the APS <inline-formula><mml:math id="M96" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi>c</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> values and the <inline-formula><mml:math id="M97" display="inline"><mml:mrow><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow><mml:mi>c</mml:mi><mml:mo>,</mml:mo><mml:mn mathvariant="normal">1.5</mml:mn></mml:mrow><mml:mi mathvariant="normal">O</mml:mi></mml:msubsup></mml:mrow></mml:math></inline-formula> time series after 20:30 UTC in Fig. 3c and d are likely the start of a CM-aerosol event which this and other evidence (see Sect. 4.1.3) suggests was a dust event. The zoomed Fig. 3d shows a rather remarkable <inline-formula><mml:math id="M98" display="inline"><mml:mrow><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow><mml:mi>c</mml:mi><mml:mo>,</mml:mo><mml:mn mathvariant="normal">1.5</mml:mn></mml:mrow><mml:mi mathvariant="normal">O</mml:mi></mml:msubsup></mml:mrow></mml:math></inline-formula> vs. <inline-formula><mml:math id="M99" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi>c</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> correlation with departures from that correlation in the neighbourhood of <inline-formula><mml:math id="M100" display="inline"><mml:mrow><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow><mml:mi>c</mml:mi><mml:mo>,</mml:mo><mml:mn mathvariant="normal">1.5</mml:mn></mml:mrow><mml:mi mathvariant="normal">O</mml:mi></mml:msubsup></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M101" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi>c</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> peaks at, respectively, <inline-formula><mml:math id="M102" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 21:30 and 00:30 UTC (the former could be ascribed to very thin cirrus clouds that we failed to detect in any satellite data while the latter could be the result of a very spatially-variable dust plume). During this particular event, two large temporal spikes were eliminated from the Level 1.0 retrievals by the AERONET temporally-driven (Level 1.5) cloud-screening algorithm (the Level 1.0 AERONET product of “Coarse AOD” can include CM cloud particles as well as CM aerosols). During this particular event, two large temporal spikes were eliminated from the Level 1.0 retrievals by the AERONET temporally-driven (Level 1.5) cloud-screening algorithm. Supporting data for this elimination<fn id="Ch1.Footn17"><p id="d2e1721">beyond the support provided in the AERONET literature for the efficacy of their cloud screening algorithm</p></fn> is presented in Figs. S9 to S11 where we demonstrate that the Level 1.0 CM AOD spikes represent cirrus clouds that temporarily fouled the CIMEL sun-pointing FOV as determined using the MISR sensor.<fn id="Ch1.Footn18"><p id="d2e1725">The MISR multi-angle (stereoscopic) capabilities permitted an estimate of the time that the roughly 8 km altitude cirrus cloud (located over Axel Heiberg Island) incited a spike in the Level 1.0 CM AOD.</p></fn></p>

      <fig id="F3" specific-use="star"><label>Figure 3</label><caption><p id="d2e1730"><bold>(a)</bold> AERONET inversion PVSDs for the claimed dust event of 21 August 2018, <bold>(b)</bold> APS hourly-averaged PVSDs at the times of the AERONET PVSDs (with standard deviations shown as error bars). Note that the APS points beyond <inline-formula><mml:math id="M103" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 3 <inline-formula><mml:math id="M104" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula> radius were either superimposed and/or free of counts in a given bin <bold>(c)</bold> SDA Level 1.5 CM AOD (<inline-formula><mml:math id="M105" display="inline"><mml:mrow><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow><mml:mi>c</mml:mi><mml:mo>,</mml:mo><mml:mn mathvariant="normal">1.5</mml:mn></mml:mrow><mml:mi mathvariant="normal">O</mml:mi></mml:msubsup></mml:mrow></mml:math></inline-formula>) and APS <inline-formula><mml:math id="M106" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi>c</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> time series and <bold>(d)</bold> a zoom of <bold>(c)</bold> at the claimed time of the dust event. The triangles shown in panel <bold>(c)</bold> indicate the approximate time of the AERONET and APS PVSDs (color coded to match the colors of the 6 PVSD cases in panels <bold>a</bold> and <bold>b</bold>). The original high-frequency 3D (1 min sample frequency) time series of APS PSDs are available upon request from the authors.</p></caption>
            <graphic xlink:href="https://amt.copernicus.org/articles/19/4553/2026/amt-19-4553-2026-f03.png"/>

          </fig>

      <p id="d2e1809">The inferred approximate position of a smaller-radius AERONET PVSD peak in Fig. 3a and the APS peak in Fig. 3b (the cyan curves at 21:00 UTC) suggests a common mode peak <inline-formula><mml:math id="M107" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 1.3–1.5 <inline-formula><mml:math id="M108" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula> (with the AERONET peaks at radii 6 <inline-formula><mml:math id="M109" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula> being outside the radius range of the APS). The 1.3–1.5 <inline-formula><mml:math id="M110" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula> peak radius is <inline-formula><mml:math id="M111" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 1.3 <inline-formula><mml:math id="M112" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula> AERONET inversion peak reported by SDN in their analysis of local dust at the Kluane Lake<fn id="Ch1.Footn19"><p id="d2e1867">This is the name AERONET ascribed to the CIMEL of the Lhù'ààn Mân' region. SDN referred to the AERONET CIMEL measurements being made at KLRS (Kluane Lake Research Station): KLRS is the acronym that we will associate with the “Kluane Lake” CIMEL</p></fn> AERONET station in the Canadian Yukon (while the 6 <inline-formula><mml:math id="M113" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula> AERONET peak is near the upper limit of the reported KLRS peak radius range from <inline-formula><mml:math id="M114" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 4 to 7 <inline-formula><mml:math id="M115" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula> for the 5 largest CM AOD cases; see Fig. 9 of that paper). However, the KLRS CM AODs were <inline-formula><mml:math id="M116" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 2 to 14 times the CM AODs of the event shown in Fig. 3c (after the onset of the significant rise around 20:30 UTC for which the CM AODs are <inline-formula><mml:math id="M117" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 0.006 to 0.016 or a <inline-formula><mml:math id="M118" display="inline"><mml:mi mathvariant="normal">Δ</mml:mi></mml:math></inline-formula>(CM AOD) <inline-formula><mml:math id="M119" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 0.01). In general, dust plumes in the Lhù'ààn Mân' region (associated with drainage basins of significantly greater relief than the region of Eureka) demonstrated a CM AOD domination relative to the dust plumes that we claim to have found at 0PAL (Fig. 3c).</p>
      <p id="d2e1928">SDN speculated that the smaller CM (1.3 <inline-formula><mml:math id="M120" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula>) AERONET-inversion peak was more likely ascribable to springtime Asian dust (while noting that the PVSDs measured with the TSI Optical Particle Sizer (OPS) device at KLRS showed no distinguishable peak that was comparable with the 1.3 <inline-formula><mml:math id="M121" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula> AERONET-inversion peak). However, the results presented in Fig. 3b suggest a <inline-formula><mml:math id="M122" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 1.4 <inline-formula><mml:math id="M123" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula> (small CM) APS peak that is clearly not due to springtime Asian dust (and thus could be ascribable to phenomenologically different dust PVSDs and CM AODs than those of the much more dynamic and optically strong KLRS site).</p>
      <p id="d2e1968">We believe that (i) the levels of PVSD-shape correspondence found between the AERONET and APS PVSDs as well as the higher-frequency temporal correspondence between the AERONET CM AOD values and the APS <inline-formula><mml:math id="M124" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi>c</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> values and (ii) the purely optical low-level plume evidence presented above for the 23 July 2007 case (the correspondence between <inline-formula><mml:math id="M125" display="inline"><mml:mrow><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mi>c</mml:mi><mml:mi mathvariant="normal">O</mml:mi></mml:msubsup></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M126" display="inline"><mml:mrow><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mi>c</mml:mi><mml:mi>l</mml:mi></mml:msubsup></mml:mrow></mml:math></inline-formula>), lend credence to a claim of having measured, two independent low-level and optically weak (local) dust events at the Eureka 0PAL site (the CIMEL <inline-formula><mml:math id="M127" display="inline"><mml:mi mathvariant="normal">Δ</mml:mi></mml:math></inline-formula>(CM AOD) increases during both events were respectively 0.007 <inline-formula><mml:math id="M128" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula> 0.004 <inline-formula><mml:math id="M129" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 0.003 and 0.016 <inline-formula><mml:math id="M130" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula> 0.006 <inline-formula><mml:math id="M131" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 0.010). The detection of such optically weak events (which effectively amount to lower limits of precision in ground-based dust AOD detectability) help to inform (appreciate certain limitations of) any satellite-based (CM AOD) search for optically detectable local dust events across the CAA. In the first instance, such weak events would seem to be detectable from a satellite sensor such as MODIS whose nominal precision appears to be significantly smaller<fn id="Ch1.Footn20"><p id="d2e2044">A nominal precision of 0.04 <inline-formula><mml:math id="M132" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M133" display="inline"><mml:mi mathvariant="normal">Δ</mml:mi></mml:math></inline-formula>AOD which for our 2018 CM AOD range yields 0.04 <inline-formula><mml:math id="M134" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 0.01 <inline-formula><mml:math id="M135" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 0.0004 (i.e. 0.04 <inline-formula><mml:math id="M136" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M137" display="inline"><mml:mi mathvariant="normal">Δ</mml:mi></mml:math></inline-formula>AOD for the best precision case of the 3 km DT over the open-ocean AOD product; Remer et al., 2013).</p></fn>. However, MODIS AOD precision is clearly an excessively optimistic (out of context) statement since that (coarse numeric scale) precision estimate in the presence of very small AODs would, no doubt, dramatically change (not to mention the fact that the nominal accuracy of the 3 km MODIS product (<inline-formula><mml:math id="M138" display="inline"><mml:mrow><mml:mo>±</mml:mo><mml:mn mathvariant="normal">0.04</mml:mn></mml:mrow></mml:math></inline-formula>) is much larger than the nominal precision).</p>
</sec>
<sec id="Ch1.S4.SS1.SSS3">
  <label>4.1.3</label><title>Satellite imagery vs. ground-based measurements at Eureka</title>
      <p id="d2e2109">The synchronicity between the CM APS <inline-formula><mml:math id="M139" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi>c</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and the <inline-formula><mml:math id="M140" display="inline"><mml:mrow><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow><mml:mi>c</mml:mi><mml:mo>,</mml:mo><mml:mn mathvariant="normal">1.5</mml:mn></mml:mrow><mml:mi mathvariant="normal">O</mml:mi></mml:msubsup></mml:mrow></mml:math></inline-formula> time series on 21 August 2018 (after 20:30 UTC) coupled with evidence of what were likely dust plumes over Eureka Sound (notably weak, grey-white plumes that appear to stretch across Eureka Sound<fn id="Ch1.Footn21"><p id="d2e2141">See Figs. S12 and S13 in the supplementary PowerPoint file “Satellite_Analysis”. The high spatial resolution (10 m pixels) of the Sentinel-S2A image and the overlain wind-vector field of Fig. S12 along with the blinking Sentinel-S2A images of 19:49 and 20:40 UTC acquisition times, suggest that dust plumes in Eureka Sound likely originated from the barren western slopes of Axel Heiberg Island.</p></fn> at and south of the entrance of Slidre Fjord) provide regional evidence for the possibility of a very weak dust event at 0PAL (that was probably incited by the strong (generally north to south) winds of Fig. S12 as they travelled over the Fosheim Peninsula landmass north of 0PAL). While Sentinel-2 clearly sees apparent dust plumes in Eureka sound (that MODIS AOD imagery suggests is <inline-formula><mml:math id="M141" display="inline"><mml:mrow><mml:mo>&lt;</mml:mo><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">0.03</mml:mn></mml:mrow></mml:math></inline-formula><fn id="Ch1.Footn22"><p id="d2e2156">Very spatially coarse AOD pixels of 3 km resolution: Eureka Sound is <inline-formula><mml:math id="M142" display="inline"><mml:mo>≲</mml:mo></mml:math></inline-formula> 3 MODIS-AOD pixels in width</p></fn>) even the Sentinel-2 imagery, would likely not detect a sub 0.01 CM AOD (the post 20:30 UTC <inline-formula><mml:math id="M143" display="inline"><mml:mrow><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow><mml:mi>c</mml:mi><mml:mo>,</mml:mo><mml:mn mathvariant="normal">1.5</mml:mn></mml:mrow><mml:mi mathvariant="normal">O</mml:mi></mml:msubsup></mml:mrow></mml:math></inline-formula> 0PAL CM AOD values of Figs. 3c and d): the explicit image evidence for weak plumes over or near the 0PAL site is ambiguous at best.</p>
      <p id="d2e2185">Figure 4 shows the temporal variation of the Eureka wind speed (ws) and wind direction for 21 and 22 August. The rapid increase at <inline-formula><mml:math id="M144" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 21:00 UTC in the <inline-formula><mml:math id="M145" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi>c</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M146" display="inline"><mml:mrow><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow><mml:mi>c</mml:mi><mml:mo>,</mml:mo><mml:mn mathvariant="normal">1.5</mml:mn></mml:mrow><mml:mi mathvariant="normal">O</mml:mi></mml:msubsup></mml:mrow></mml:math></inline-formula> time series of Fig. 3c is within the period of significantly high-amplitude ws values from 18:00 on 21 August to 18:00 on 22 August (the red-filled points of Fig. 4). This behavior is broadly consistent with CARRA (Copernicus Arctic Regional Reanalysis) near-surface simulations in the neighbourhood of Eureka Sound to the west of 0PAL (the region of the 21 August dust plumes in the Sentinel-2 image of Fig. S12). We would argue, based on the CARRA spatio-temporal simulations of generally weaker ws values at 18:00 UTC to generally stronger values at 21:00 UTC over the Eureka Sound/0PAL region<fn id="Ch1.Footn23"><p id="d2e2224">as per Figs. S32g and S32h of the Supplementary PowerPoint file “CARRA_wind_ simulations”</p></fn>, that a significantly strong regional wind event<fn id="Ch1.Footn24"><p id="d2e2228">Roughly (qualitatively) lasting from 18:00 on 21 August (Fig. 32g) to 06:00 on 23 August (Fig. 32s).</p></fn> incited the Eureka Sound 21 August dust plumes and the attendant <inline-formula><mml:math id="M147" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi>c</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M148" display="inline"><mml:mrow><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow><mml:mi>c</mml:mi><mml:mo>,</mml:mo><mml:mn mathvariant="normal">1.5</mml:mn></mml:mrow><mml:mi mathvariant="normal">O</mml:mi></mml:msubsup></mml:mrow></mml:math></inline-formula> increases near 0PAL (the latter plumes likely being induced by northerly winds traversing the slopes of the Fosheim Peninsula).</p>

      <fig id="F4"><label>Figure 4</label><caption><p id="d2e2264">Temporal variation of the wind speed and wind direction for 21 and 22 August 2018 (data from the ECCC “Eureka Climate” station very near 0PAL). The wind direction is defined as the direction that the wind is coming from relative to the station meridian. Positive and negative wind directions refer to CW and CCW angular departures from the meridian. The red-filled points indicate wind speeds that are above the mean <inline-formula><mml:math id="M149" display="inline"><mml:mo>+</mml:mo></mml:math></inline-formula> standard deviation (15.5 <inline-formula><mml:math id="M150" display="inline"><mml:mo>+</mml:mo></mml:math></inline-formula> 2.5 <inline-formula><mml:math id="M151" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 18 km h<sup>−1</sup>) value of the Eureka (August) windspeed climatology reported in Fig. 5 of Lesins et al. (2010). The dashed vertical line shows a time (21:00 UTC) that is representative of the significant rise in CM AOD (<inline-formula><mml:math id="M153" display="inline"><mml:mrow><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow><mml:mi>c</mml:mi><mml:mo>,</mml:mo><mml:mn mathvariant="normal">1.5</mml:mn></mml:mrow><mml:mi mathvariant="normal">O</mml:mi></mml:msubsup></mml:mrow></mml:math></inline-formula>) and APS <inline-formula><mml:math id="M154" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi>c</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> values in Fig. 3.</p></caption>
            <graphic xlink:href="https://amt.copernicus.org/articles/19/4553/2026/amt-19-4553-2026-f04.png"/>

          </fig>

</sec>
</sec>
<sec id="Ch1.S4.SS2">
  <label>4.2</label><title>Satellite-based RS of local dust events across the CAA</title>
      <p id="d2e2345">We employed satellite-based RS to investigate potential dust events over CAA sites where there was no ground-based sensors. Our goal here was to gain more insight into satellite-based RS capabilities in different types of Arctic environments. A strong motivation for the CAA analysis was our belief that satellite-based dust RS findings over a variety of CAA sites would help build confidence in the satellite-based RS of dust events in general and weaker dust events in particular. Each one of our dust event cases below includes a small CAA map with the position of the event indicated by a green star.</p>
<sec id="Ch1.S4.SS2.SSS1">
  <label>4.2.1</label><title>Large-scale dust event in the northern part of the CAA</title>
      <p id="d2e2355">Figure 5a shows an Aqua true color image<fn id="Ch1.Footn25"><p id="d2e2358">Acquired at 15:20 UTC (late morning local time) on 8 September 2020</p></fn> of a dust plume that appears to originate from Axel Heiberg Island<fn id="Ch1.Footn26"><p id="d2e2362">it appears to be emanating from the largely barren drainage basin whose watershed empties into Eureka Sound (see Fig. S15 for details).</p></fn> and flow along the open water of Eureka Sound and Greely Fjord. The thumbnail images of Figs. 5b and c show respectively, the MODIS-Aqua AOD and CM AODs (3 km resolution product) superimposed on the color image. Figure S14a<fn id="Ch1.Footn27"><p id="d2e2366">Supplementary PowerPoint file “Satellite_Analysis”</p></fn> shows a zoom of the Aqua color image blinking with the AOD and CM AOD products alongside a map of the region (we recommend looking at such zooms for details). The plume is most evident as it crosses Greely Fjord along its northeastward path and then appears to veer northwestward towards the coast of the Svartfjeld Peninsula. This flow pattern is generally supported by the surface ws vector field of Fig. S14b (including a final CCW turning (backing) in Greely Fjord followed by a CW turn (veering) of the dust plume towards Svartfjeld Peninsula<fn id="Ch1.Footn28"><p id="d2e2370">There are no MINX (MISR) plume height or speed retrievals to report because the plume was basically obscured by clouds at the MISR orbit time of 19:50 UTC.</p></fn>). The CM AOD values of Fig. S14a show a spatial pattern that includes a band of moderately stronger CM AOD values which are coherent with the northeast-flowing spatial pattern of greyish intensity variations in the true-color image (less evident but still notable is the CM AOD and greyish-intensity pattern matching of the weaker plume that has veered in the northwesterly direction). The CM AOD values vary from extremes of <inline-formula><mml:math id="M155" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 0.02 to 0.31 (AOD extremes of 0.06 to 0.42).</p>

      <fig id="F5" specific-use="star"><label>Figure 5</label><caption><p id="d2e2383"><bold>(a)</bold> MODIS Aqua true color image acquired at 15:20 UTC on 8 September 2020, <bold>(b, c)</bold> MODIS Aqua AOD product and derived CM AOD products respectively (superimposed on the true color image: see Fig. S14a for a detailed (zoomed) overlain comparison of panels <bold>a</bold>–<bold>c</bold>). See Sect. 3.4.1 above for the expression relating CM AOD to AOD.</p></caption>
            <graphic xlink:href="https://amt.copernicus.org/articles/19/4553/2026/amt-19-4553-2026-f05.png"/>

          </fig>

</sec>
<sec id="Ch1.S4.SS2.SSS2">
  <label>4.2.2</label><title>Dust event in the central southern part of the CAA</title>
      <p id="d2e2411">Figure 6a shows a (26 September 2015) MODIS-Terra, true color image of local dust plumes apparently emanating from Prince of Wales Island (in the central southern part of the CAA) and moving in a northwesterly direction towards Victoria Island (image acquired at 19:10 UTC). The true color image, along with the MODIS AOD products of Figs. 6b and c, supported by the MISR stereoscopic multi-look animation (see Fig. S16<fn id="Ch1.Footn29"><p id="d2e2414">Supplementary PowerPoint file “Satellite_Analysis”</p></fn> and its caption for details) reaffirm the presence of dust plumes flowing in a northwesterly direction. The color image and MODIS AOD products of Fig. 6 (see Fig. S17 for greater detail) support a claim of distinct individual dust plumes. The CM AOD and AOD values of the plumes (whose spatial variation is visually coherent with the variations of the plume-like structure seen in the color image) vary respectively, across extremes of 0.02 to 0.56 and 0.06 to 0.73). The landcover map (Fig. S18) shows a 20 km wide barren region which appears to be the dominating influence as the source of the dust plumes (judging by the color image combined with the MODIS AOD product).</p>

      <fig id="F6" specific-use="star"><label>Figure 6</label><caption><p id="d2e2420">Local dust event (over Prince of Wales Island and Victoria Island) captured on 26 September 2015. <bold>(a)</bold> MODIS Terra true-color image acquired at 19:10 UTC <bold>(b)</bold> AOD product, <bold>(c)</bold> CM AOD. Note that there appear to be distinct water plumes before and after the barren region on Prince of Wales Island (water plumes that were captured by the MODIS cloud OD product and are distinctly unique in the color image).</p></caption>
            <graphic xlink:href="https://amt.copernicus.org/articles/19/4553/2026/amt-19-4553-2026-f06.png"/>

          </fig>

      <p id="d2e2438">A sampled MISR trajectory in the direction of the dust plume (the orange-colored trajectory on the MISR color image of Fig. 7a) shows wind-corrected plume height along that trajectory while Fig. 7b and c show, respectively, plume heights as a function of trajectory-sample number and the plume heights histogram. The analogous pair of trajectory and histogram graphs for plume speed are shown in Fig. 7d and e. The average MINX (MISR) plume height <inline-formula><mml:math id="M156" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> its standard deviation is 298 <inline-formula><mml:math id="M157" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 230 m a.s.l.<fn id="Ch1.Footn30"><p id="d2e2455">We note that in general, neither the plume height or the plume speed sampling trajectories are subject to any objective sampling protocol and that the plume height (and plume speed) histograms generally represent significant departures from a normal distribution. While we report means and standard deviations of plume height and wind speed, they are meant to be order-of-magnitude height and height variability indicators for subjectively selected plume structures seen in the color imagery.</p></fn>. The mean and standard deviation of the MISR wind (plume) speed histogram (<inline-formula><mml:math id="M158" display="inline"><mml:mrow><mml:mo>〈</mml:mo><mml:mtext>ws</mml:mtext><mml:mo>〉</mml:mo><mml:mo>±</mml:mo><mml:mi mathvariant="italic">σ</mml:mi><mml:mfenced open="(" close=")"><mml:mtext>ws</mml:mtext></mml:mfenced><mml:mo>=</mml:mo><mml:mn mathvariant="normal">75</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">24</mml:mn></mml:mrow></mml:math></inline-formula> km h<sup>−1</sup> or 54 <inline-formula><mml:math id="M160" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 17 km h<sup>−1</sup> when normalized to near surface conditions<fn id="Ch1.Footn31"><p id="d2e2518">An ECCC met station (WMO ID: 71017, coordinates 73° 46<sup>′</sup> N, 105° 18<sup>′</sup> ) at 11 m elevation is located on Stefansson Island (see Fig. 6). We normalized the MISR plume speed to the plume speed at the elevation of the station by applying a standard wind gradient expression (see e.g. Kaltschmitt et al., 2007) with an open-water wind shear (Hellman) exponent of 0.1: <inline-formula><mml:math id="M164" display="inline"><mml:mrow><mml:mtext>ws</mml:mtext><mml:mo>(</mml:mo><mml:mi>h</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:msub><mml:mtext>ws</mml:mtext><mml:mi mathvariant="normal">ref</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>h</mml:mi><mml:mo>/</mml:mo><mml:msub><mml:mi>h</mml:mi><mml:mi mathvariant="normal">ref</mml:mi></mml:msub><mml:msup><mml:mo>)</mml:mo><mml:mi>a</mml:mi></mml:msup></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M165" display="inline"><mml:mrow><mml:msub><mml:mtext>ws</mml:mtext><mml:mi mathvariant="normal">ref</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mtext>ws</mml:mtext><mml:mo>(</mml:mo><mml:mi>h</mml:mi><mml:mo>)</mml:mo><mml:mo>(</mml:mo><mml:mi>h</mml:mi><mml:mo>/</mml:mo><mml:msub><mml:mi>h</mml:mi><mml:mi mathvariant="normal">ref</mml:mi></mml:msub><mml:msup><mml:mo>)</mml:mo><mml:mrow><mml:mo>-</mml:mo><mml:mi>a</mml:mi></mml:mrow></mml:msup><mml:mo>=</mml:mo><mml:mn mathvariant="normal">75</mml:mn><mml:mo>(</mml:mo><mml:mn mathvariant="normal">298</mml:mn><mml:mo>/</mml:mo><mml:mn mathvariant="normal">11</mml:mn><mml:msup><mml:mo>)</mml:mo><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.1</mml:mn></mml:mrow></mml:msup><mml:mo>=</mml:mo><mml:mn mathvariant="normal">54</mml:mn></mml:mrow></mml:math></inline-formula></p></fn>). This <inline-formula><mml:math id="M166" display="inline"><mml:mrow><mml:mo>〈</mml:mo><mml:mtext>ws</mml:mtext><mml:mo>〉</mml:mo></mml:mrow></mml:math></inline-formula> value is <inline-formula><mml:math id="M167" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> the 19:00 UTC 26 September 2015 Stefansson Island met station ws value of 49 km h<sup>−1</sup> and <inline-formula><mml:math id="M169" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 3-times the (2002–2024) Stefansson Island climatological mean for the month of September (17.7 <inline-formula><mml:math id="M170" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 10.9 km h<sup>−1</sup>).</p>

      <fig id="F7" specific-use="star"><label>Figure 7</label><caption><p id="d2e2702"><bold>(a)</bold> MISR nadir (An camera) true color image acquired at 19:12 UTC (275 m resolution) with retrieved MISR plume height values along a selected trajectory (the red-orange path that begins with a yellow star and whose color legend appears to the right of the image) superimposed on the color image, <bold>(b)</bold> trajectory plume heights as a function of distance from the reference point (yellow star) and <bold>(c)</bold> the histogram of those selected plume heights. <bold>(d, e)</bold> Graphs are the corresponding wind (plume) speed trajectory values and histogram. We note that the MINX assumption of no vertical plume motion may reduce the plume height retrieval accuracy (Nelson et al., 2013).</p></caption>
            <graphic xlink:href="https://amt.copernicus.org/articles/19/4553/2026/amt-19-4553-2026-f07.png"/>

          </fig>

</sec>
<sec id="Ch1.S4.SS2.SSS3">
  <label>4.2.3</label><title>Dust event in the southwest corner of the CAA</title>
      <p id="d2e2730">The red arrows of Fig. 8a delineate what we argue are a pair of local dust plumes emanating from largely vegetation-free areas on Banks Island (the southwest corner of the CAA) and flowing south over the Amundsen Gulf (MODIS-Terra color image acquired at 20:20 UTC on 1 October 2018). Some plume widths are sufficiently thin that the moderate resolution MODIS and MISR color imagery (as well as the coarser resolution of the MODIS 3 km AOD product) diffuses out much of the fine spatial detail. The AOD product and the derived CM AOD (Fig. 8b and c) appear to capture the general individual plume patterns seen in the color imagery (and their apparent broadening into a single plume). The MODIS CM AOD values in the vicinity of those plumes range from <inline-formula><mml:math id="M172" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 0.03 to 0.26 (while AOD values range from <inline-formula><mml:math id="M173" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 0.04 to 0.37).</p>

      <fig id="F8" specific-use="star"><label>Figure 8</label><caption><p id="d2e2749"><bold>(a)</bold> Local dust plumes emanating from Banks Island on 1 October 2018 (MODIS Terra true color image acquired at 20:20 UTC). Panels <bold>(b)</bold> and <bold>(c)</bold> show the MODIS Terra AOD and the derived CM AOD superimposed on the color image.</p></caption>
            <graphic xlink:href="https://amt.copernicus.org/articles/19/4553/2026/amt-19-4553-2026-f08.png"/>

          </fig>

      <p id="d2e2766">This was a complicated case with high altitude cirrus being (at least qualitatively) confused with the very low altitude dust plumes. The issue can, on a visual level, be resolved by deferring to animations of the multi-angle MISR views where the separation of the former from the latter (in terms of their apparent stereoscopic ground speed relative to the fixed ground scene) is evident (see that animation in Fig. S19). Figure S20 shows a sampling trajectory of the double dust plumes that are pointed to by the red arrows of Fig. 8a. The mean and standard deviation of the MISR plume height and wind (plume) speed histograms along this trajectory are respectively 196 <inline-formula><mml:math id="M174" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 155 and 25 <inline-formula><mml:math id="M175" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 25 km h<sup>−1</sup> (the latter value belonging to a distinctly non-normal distribution).</p>
      <p id="d2e2796">The geographic details of the two thin dust plumes seen in the MODIS-Terra color image of Fig. 8a along with even weaker and thinner dust plumes elsewhere in the region are brought into rather striking relief in zooms of a high-resolution Sentinel-2 image. Figure S21 shows, what amounts to, apparent source information for five different plumes (including source information for one of the two thin dust plumes seen in the MODIS image). Those zoomed images give valuable, if indirect, contextual information on the source and dynamics of the plumes. One can, for all five cases, see a water to land dust plume continuity with the plume origins being either (a) very low altitude dust plumes over the land or (b) surface features of the sources.</p>
</sec>
<sec id="Ch1.S4.SS2.SSS4">
  <label>4.2.4</label><title>Dust plumes emanating from Ellef Ringnes Island (eastern part of the central CAA)</title>
      <p id="d2e2808">The 20:10 UTC, 13 September 2014 MODIS-Terra true color image of Fig. 9a shows what appear to be local dust plumes emanating from dark brown regions of Meteorologist Peninsula<fn id="Ch1.Footn32"><p id="d2e2811">Meteorologist Peninsula is located at the extreme south of Ellef Ringnes Island (again, see Fig. 9a)</p></fn> and flowing over the open-water region at the southern tip of that peninsula. Figure 9b and c show the MODIS AOD product and estimated CM AODs over a part of that open-water region: the spatial variation of those AODs and CM AODs are qualitatively coherent with the perceived spatial variations of the dust plumes in the true color image of Fig. 9a. Figure S23 shows zoomed-in details: one can observe that the thickest part of the plumes as seen on the color image and the largest CM AODs are aligned with the brownish regions (presumably sources) on Meteorologist Peninsula. CM AOD values in Fig. 8b and c range from <inline-formula><mml:math id="M177" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 0.05 to 0.47 while the AOD values range from <inline-formula><mml:math id="M178" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 0.11 to 0.50.</p>

      <fig id="F9" specific-use="star"><label>Figure 9</label><caption><p id="d2e2831">MODIS-Terra true color imagery (logarithmic enhancement) acquired at 20:10 UTC over Ellef Ringnes Island on 13 September 2014 <bold>(a)</bold> local dust plumes over the water emanating from Meteorologist Peninsula on Ellef Ringnes Island. Panels <bold>(b)</bold> and <bold>(c)</bold> show the MODIS Terra AOD and derived CM AOD superimposed on the color image (see Fig. S23 in the PowerPoint file “Satellite_Analysis” of Sayedain and O'Neill, 2026, for a full resolution comparison of the AODs and the color image).</p></caption>
            <graphic xlink:href="https://amt.copernicus.org/articles/19/4553/2026/amt-19-4553-2026-f09.png"/>

          </fig>

      <p id="d2e2849">Figures S24 and S25 show a selected MISR trajectory case over the open water west of Meteorologist Peninsula (Fig. S22 shows the [subjective] investigation that was carried out to determine the color image enhancement that best permitted one to appreciate how the trajectory was embedded in the dust plume<fn id="Ch1.Footn33"><p id="d2e2852">Figure S24 shows the MISR camera animation where one can more readily appreciate the positions and stereoscope movement of higher altitude clouds.</p></fn>). The mean wind-corrected plume height is 264 <inline-formula><mml:math id="M179" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 162 m for the trajectory while the mean plume speed is 38 <inline-formula><mml:math id="M180" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 14 km h<sup>−1</sup>. Normalizing the latter value to the height of the nearest met station<fn id="Ch1.Footn34"><p id="d2e2882">The 58 m ECCC met station of “ISACHSEN (AUT)” in the north of Ellef Ringnes Island (78° 47<sup>′</sup> N, 103° 33<sup>′</sup> W). The normalization approximation for wind-shear (wind gradient) effects was carried out as per Sect. 4.2.2 above.</p></fn> yields normalized wind speeds of 32 km h<sup>−1</sup>. This is moderately lower than the 20:20 AUT met station value of 51 km h<sup>−1</sup> and 1.7-times its climatologically (1996–2025) mean wind speed for the month of September (18.8 <inline-formula><mml:math id="M186" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 13.5 km h<sup>−1</sup>).</p>
      <p id="d2e2949">In the absence of a standard AOD product we developed an ad hoc AOD retrieval technique for the dirty brown snow/ice region between Meteorologist Peninsula and King Christian Island (see Fig. S26 and its caption for details on that ad hoc technique). The results of that retrieval showed a coarse degree of AOD continuity across the ice/snow to water interface<fn id="Ch1.Footn35"><p id="d2e2952">there is no CM AOD option for the snow/ice retrievals since we have no CMF estimate for those retrievals</p></fn> (see the blinking animation of Fig. S27). Evidence that the dirty brown area was (at least in part) a dust plume and not deposited dust is provided by a MISR height profile showing plume heights varying between 0 to <inline-formula><mml:math id="M188" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 500 m (Fig. S28). The corresponding plume speeds of 42 <inline-formula><mml:math id="M189" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 20 km h<sup>−1</sup> are moderately greater than the plume speeds over water.</p>
</sec>
</sec>
<sec id="Ch1.S4.SS3">
  <label>4.3</label><title>Surface plume deposition/snow melt; snow/ice reflectance changes as optical precursors of dust plumes</title>
      <p id="d2e2991">The RS of airborne Arctic dust can be advantageously complemented by the RS of reflectance changes (darkening) induced by the deposition of airborne dust on snow or ice and/or reduced reflectance incited by premature snow melt due to dust deposition. Woo et al. (1991) noted that the presence of snow-melt zones over the Fosheim Peninsula on Ellesmere Island corresponded to dark spots in early AVHRR imagery. Ranjbar et al. (2021) found roughly the same dark patterns in true color MODIS imagery and showed visual evidence of deposition of dust on snow (or underlying soil subsequent to snow melt) in a mosaic of true color MODIS imagery acquired over the whole of Ellesmere Island.</p>
      <p id="d2e2994">O'Neill et al. (2025) argued that the combination of persistent day to day dark zones in MODIS imagery and the lack of movement of those features in MISR multi-angle imagery was indicative of local-dust surface deposition in the case of Prince Patrick Island and neighbouring Eglinton Island (west central CAA). We found what appeared to be a more dynamic MISR example of deposited dust across the Strand Bay region of Axel Heiberg Island over a three-day period (see Fig. S29). Figure S30a shows the MISR height profile of a 8 June 2007, airborne dust plume and the position of its sampling trajectory on the associated MISR (nadir) image<fn id="Ch1.Footn36"><p id="d2e2997">The MISR image shows numerous dust plumes which appear to be associated with dark sources on the southern shore of Strand Bay.</p></fn>. The plume profile of Fig. S30b (acquired 2 d later) shows what appears to be near-zero heights in a region where the color image indicates a much darker pattern than that of Fig. S30a<fn id="Ch1.Footn37"><p id="d2e3001">Note that the MISR times of S30a and S30b images are nearly identical (solar illumination conditions are nearly identical)</p></fn> (accompanied by a rise in plume height near the northern shore of Strand Bay). We would suggest that the darkest region of Strand Bay in the color image is likely a dynamic example of the process of dust deposition. In this particular case, the source of the (very dark) dust is likely the volcanic deposits known to characterize much of the Strand Fjord Formation (Williamson and MacRae, 2015).</p>
</sec>
</sec>
<sec id="Ch1.S5" sec-type="conclusions">
  <label>5</label><title>Conclusions</title>
      <p id="d2e3014">Ground-based RS and microphysical measurements acquired at the PEARL complex in Eureka were employed to investigate the potential for satellite-based and ground-based RS of local dust plumes. This analysis supported and/or complemented explicit examples of satellite-based RS of local dust events near Eureka and across the CAA.</p>
      <p id="d2e3017">Ground-based RS validation results were obtained (in terms of the identification and characterization of local dust events) with significant correlations in 2007 data between the 0PAL (ground-based) CM AOD and the lidar-derived CM AOD (and the lack of correlation with the 615 m above-plume CM AOD at the Ridge Lab). The late-summer correlations (21 August 2018 data) between APS CM particle-volume concentration (<inline-formula><mml:math id="M191" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi>c</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) measurements and 0PAL CM AODs along with the similarity between the APS and AERONET PVSDs suggest a significant 1.3–1.5 <inline-formula><mml:math id="M192" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula> radius peak that was due to local dust of weak CM AOD (<inline-formula><mml:math id="M193" display="inline"><mml:mrow><mml:mo>&lt;</mml:mo><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">0.01</mml:mn></mml:mrow></mml:math></inline-formula>). This is notable given the near-1.3 <inline-formula><mml:math id="M194" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula> radius AERONET peaks reported by SDN for a springtime (May) measurement campaign at the KLRS site in the Yukon (a peak which they ascribed to springtime Asian dust).</p>
      <p id="d2e3063">Indirect linkages were made between the surface RS and microphysical data and available satellite on 21 August 2018, RS imagery acquired in the neighbourhood of Eureka: we argued that a weak but detectable plume over Eureka Sound (MODIS AODs <inline-formula><mml:math id="M195" display="inline"><mml:mrow><mml:mo>&lt;</mml:mo><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">0.1</mml:mn></mml:mrow></mml:math></inline-formula>) might be related to the very weak CM AODs measured by the 0PAL CIMEL (values of <inline-formula><mml:math id="M196" display="inline"><mml:mrow><mml:mo>&lt;</mml:mo><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">0.01</mml:mn></mml:mrow></mml:math></inline-formula> that are typically undetectable by satellite RS). More direct linkages were made with 0PAL wind speed (ws) measurements and regional ws (reanalysis) values. It was argued that above normal 0PAL ws values and above normal regional ws values coupled with co-incident increases in CM AOD and <inline-formula><mml:math id="M197" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi>c</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mn mathvariant="normal">0</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> measurements at 0PAL were evidence of a region-wide wind event that caused local and regional dust disturbances.</p>

<table-wrap id="T1" specific-use="star"><label>Table 1</label><caption><p id="d2e3111">Summary of CAA dust events captured using satellite-based RS. See footnote 37 concerning the reporting of means and standard deviations for plume height and plume speed.</p></caption><oasis:table frame="topbot"><oasis:tgroup cols="8">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="left"/>
     <oasis:colspec colnum="3" colname="col3" align="right"/>
     <oasis:colspec colnum="4" colname="col4" align="right"/>
     <oasis:colspec colnum="5" colname="col5" align="right"/>
     <oasis:colspec colnum="6" colname="col6" align="right"/>
     <oasis:colspec colnum="7" colname="col7" align="right"/>
     <oasis:colspec colnum="8" colname="col8" align="right"/>
     <oasis:thead>
       <oasis:row>
         <oasis:entry colname="col1">Source location</oasis:entry>
         <oasis:entry colname="col2">Date and time</oasis:entry>
         <oasis:entry colname="col3">Approximate</oasis:entry>
         <oasis:entry colname="col4">AOD</oasis:entry>
         <oasis:entry colname="col5">CM</oasis:entry>
         <oasis:entry colname="col6">Visible</oasis:entry>
         <oasis:entry colname="col7"/>
         <oasis:entry colname="col8"/>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">(Island)</oasis:entry>
         <oasis:entry colname="col2">(dd/mm/yyyy,</oasis:entry>
         <oasis:entry colname="col3">coordinates of</oasis:entry>
         <oasis:entry colname="col4">(min,</oasis:entry>
         <oasis:entry colname="col5">AOD</oasis:entry>
         <oasis:entry colname="col6">plume</oasis:entry>
         <oasis:entry colname="col7">plume</oasis:entry>
         <oasis:entry colname="col8">plume</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2">hh:mm)</oasis:entry>
         <oasis:entry colname="col3">plume source</oasis:entry>
         <oasis:entry colname="col4">max)</oasis:entry>
         <oasis:entry colname="col5">(min,</oasis:entry>
         <oasis:entry colname="col6">length</oasis:entry>
         <oasis:entry colname="col7">height</oasis:entry>
         <oasis:entry colname="col8">speed</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2">[UTC]</oasis:entry>
         <oasis:entry colname="col3">(lat, long) [°]</oasis:entry>
         <oasis:entry colname="col4"/>
         <oasis:entry colname="col5">max)</oasis:entry>
         <oasis:entry colname="col6">[km]</oasis:entry>
         <oasis:entry colname="col7">(a.s.l.)</oasis:entry>
         <oasis:entry colname="col8">[km h<sup>−1</sup>]</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2"/>
         <oasis:entry colname="col3"/>
         <oasis:entry colname="col4"/>
         <oasis:entry colname="col5"/>
         <oasis:entry colname="col6"/>
         <oasis:entry colname="col7">[m]</oasis:entry>
         <oasis:entry colname="col8"/>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>
         <oasis:entry colname="col1">Axel Heiberg Island</oasis:entry>
         <oasis:entry colname="col2">08/09/2020, 15:20</oasis:entry>
         <oasis:entry colname="col3">(80.05, <inline-formula><mml:math id="M199" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>87.55)</oasis:entry>
         <oasis:entry colname="col4">(0.06, 0.42)</oasis:entry>
         <oasis:entry colname="col5">(0.02, 0.31)</oasis:entry>
         <oasis:entry colname="col6">60</oasis:entry>
         <oasis:entry colname="col7">NA</oasis:entry>
         <oasis:entry colname="col8">NA</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Prince of Wales Island</oasis:entry>
         <oasis:entry colname="col2">26/09/2015, 19:10</oasis:entry>
         <oasis:entry colname="col3">(72.65, <inline-formula><mml:math id="M200" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>102.36)</oasis:entry>
         <oasis:entry colname="col4">(0.06, 0.73)</oasis:entry>
         <oasis:entry colname="col5">(0.02, 0.56)</oasis:entry>
         <oasis:entry colname="col6">110</oasis:entry>
         <oasis:entry colname="col7">300 <inline-formula><mml:math id="M201" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 230</oasis:entry>
         <oasis:entry colname="col8">75 <inline-formula><mml:math id="M202" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 24</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Banks Island</oasis:entry>
         <oasis:entry colname="col2">01/10/2018, 20:20</oasis:entry>
         <oasis:entry colname="col3">(71.46, <inline-formula><mml:math id="M203" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>121.74)</oasis:entry>
         <oasis:entry colname="col4">(0.04, 0.37)</oasis:entry>
         <oasis:entry colname="col5">(0.03, 0.26)</oasis:entry>
         <oasis:entry colname="col6">50</oasis:entry>
         <oasis:entry colname="col7">196 <inline-formula><mml:math id="M204" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 155</oasis:entry>
         <oasis:entry colname="col8">25 <inline-formula><mml:math id="M205" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 25</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Ellef Ringnes Island</oasis:entry>
         <oasis:entry colname="col2">13/09/2014, 20:10</oasis:entry>
         <oasis:entry colname="col3">(77.83, <inline-formula><mml:math id="M206" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>99.50)</oasis:entry>
         <oasis:entry colname="col4">(0.11, 0.50)</oasis:entry>
         <oasis:entry colname="col5">(0.05, 0.47)</oasis:entry>
         <oasis:entry colname="col6">60</oasis:entry>
         <oasis:entry colname="col7">264 <inline-formula><mml:math id="M207" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 162</oasis:entry>
         <oasis:entry colname="col8">38 <inline-formula><mml:math id="M208" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 14</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Axel Heiberg Island (Strand Bay)</oasis:entry>
         <oasis:entry colname="col2">08/06/2007, 19:59</oasis:entry>
         <oasis:entry colname="col3">(79, <inline-formula><mml:math id="M209" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>93.25)</oasis:entry>
         <oasis:entry colname="col4">NA</oasis:entry>
         <oasis:entry colname="col5">NA</oasis:entry>
         <oasis:entry colname="col6">20</oasis:entry>
         <oasis:entry colname="col7">165 <inline-formula><mml:math id="M210" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 99</oasis:entry>
         <oasis:entry colname="col8">1.6 <inline-formula><mml:math id="M211" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 1.2</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Axel Heiberg Island (Strand Bay)</oasis:entry>
         <oasis:entry colname="col2">10/06/2007, 19:47</oasis:entry>
         <oasis:entry colname="col3">(79, <inline-formula><mml:math id="M212" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>93.25)</oasis:entry>
         <oasis:entry colname="col4">NA</oasis:entry>
         <oasis:entry colname="col5">NA</oasis:entry>
         <oasis:entry colname="col6">20</oasis:entry>
         <oasis:entry colname="col7">40 <inline-formula><mml:math id="M213" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 40</oasis:entry>
         <oasis:entry colname="col8">2 <inline-formula><mml:math id="M214" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 2</oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table></table-wrap>

      <p id="d2e3563">A pan-CAA analysis using the multi-dimensional information available from MODIS color imagery and its AOD products, MISR multi-camera, stereoscopic imagery, MINX (MISR) estimates of plume height and speed and high spatial resolution Sentinel-2 imagery supported by measured and/or regional ws products indicated that local dust plumes of relatively weak to strong optical thickness (CM AOD ranging from <inline-formula><mml:math id="M215" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 0.02 to 0.60) at generally sub-km plume heights could be detected from available satellite products. A sampling of key parameters for all plume events is given in Table 1. In what follows we give a summary of those pan-CAA conclusions.</p>
      <p id="d2e3573">A 20 September 2020 plume event north of the Fosheim Peninsula showed evidence of plume dynamics that were roughly coherent with CARRA wind vector patterns and whose spatial variation (colour image pattern) was similar to the spatial pattern of the derived CM AODs. The MINX (MISR) plume height and speed of (26 September 2015) dust plumes flowing from Prince of Wales Island to Victoria Island (southern part of the CAA) were 300 <inline-formula><mml:math id="M216" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 230 m a.s.l. and 75 <inline-formula><mml:math id="M217" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 24 km h<sup>−1</sup> (while MODIS CM AOD values ranged from 0.02 to 0.56). The 54 km h<sup>−1</sup> value<fn id="Ch1.Footn38"><p id="d2e3614">the measured value normalized to the height of the nearby met station</p></fn> for that event is abnormally large (3 times the climatological mean for September).</p>
      <p id="d2e3618">Information from MISR, MODIS and Sentinel-2 color imagery was employed to identify dust plumes (partially obscured by higher altitude clouds) emanating from local dust sources on Banks Island (southwest corner of the CAA) in October of 2018. The MODIS CM AOD values, for the Banks Island satellite events varied from to 0.03 to 0.26 and visually corresponded to what appeared to be dust plumes in the MODIS color imagery (supported by the stereoscopically determined distinctions between clouds and low-level plumes provided by the MISR imagery). The Sentinel-2 color imagery provided a unique high-spatial-resolution perspective that enabled the distinction of the land to water continuity of a few local dust plumes. A moderately strong dust event emanating from Ellef Ringnes Island in September of 2014 was characterized by CM AODs between <inline-formula><mml:math id="M220" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 0.05 to 0.47, mean plume heights of <inline-formula><mml:math id="M221" display="inline"><mml:mrow><mml:mo>&lt;</mml:mo><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">300</mml:mn></mml:mrow></mml:math></inline-formula> m and mean plume speed (normalized to the elevation of the nearby met station) of 32 <inline-formula><mml:math id="M222" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 12 km h<sup>−1</sup> (1.7 times the climatological mean of the nearby [Stefansson Island] met station for the month of September).</p>
      <p id="d2e3659">We employed MINX (MISR) color imagery and plume height retrievals to argue that June 2007 Strand Bay (Axel Heiberg Island) MISR images of a dirty snow/ice surface showed both a plume above the surface and what appeared to be plume deposition (zero altitude plume retrievals) over the surface 2 d later (with a much darker reflectance). This appears to be a rather rare example of a commonly cited phenomenon (dust plume deposition effects). The RS identification of dust deposition events on snow presents a unique opportunity for monitoring the attendant changes in snow reflectance (and premature snow melt events) across different Arctic regions.</p>
      <p id="d2e3662">In summary, a series of dust events involving distinct, narrow plumes, at least partly over dark water, downwind of likely dust sources and typically under contemporaneous high-wind conditions were identified. The use of the MODIS and/or MISR and/or Sentinel-2 imagery (coupled with geographical and meteorological information) for identifying and characterizing local dust plumes requires careful analysis: however, the benefits often include a synergistic characterization of plume properties that significantly exceed what can be extracted from a single sensor. The specialized advantages of each of these RS sensors should be understood before undertaking such an approach: our greatest strategic realization, for example, was that, in spite of the obvious advantages of the CALIOP lidar in characterizing dust plume properties, the MISR imager has a much greater chance of detecting a spatially constrained plume (CALIOP being limited to a single orbit line rather than broad, along-track, MISR images).</p>
</sec>

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

<app id="App1.Ch1.S1">
  <label>Appendix A</label><title/>
<sec id="App1.Ch1.S1.SS1">
  <label>A1</label><title>Comparing CIMEL- and AHSRL-derived AODs</title>
<sec id="App1.Ch1.S1.SS1.SSS1">
  <label>A1.1</label><title>CIMEL-based FM and CM attribution</title>
      <p id="d2e3689">Given the unique arrangement of the two CIMELs at Eureka, one near the 0PAL site (superscript “O” and one at the higher altitude PEARL (Ridge lab) site (“P” subscript), the (500 nm) FM, CM and total AODs of the layer between the two sites (assuming optical homogeneity above P between the two different lines of site) are,
            

                  <disp-formula id="App1.Ch1.S1.E1" specific-use="gather" content-type="subnumberedon"><mml:math id="M224" display="block"><mml:mtable displaystyle="true"><mml:mlabeledtr id="App1.Ch1.S1.E1.2"><mml:mtd><mml:mtext>A1a</mml:mtext></mml:mtd><mml:mtd><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mi>f</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mi>f</mml:mi><mml:mi mathvariant="normal">O</mml:mi></mml:msubsup><mml:mo>-</mml:mo><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mi>f</mml:mi><mml:mi mathvariant="normal">P</mml:mi></mml:msubsup></mml:mrow></mml:mtd></mml:mlabeledtr><mml:mlabeledtr id="App1.Ch1.S1.E1.3"><mml:mtd><mml:mtext>A1b</mml:mtext></mml:mtd><mml:mtd><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mi>c</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mi>c</mml:mi><mml:mi mathvariant="normal">O</mml:mi></mml:msubsup><mml:mo>-</mml:mo><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mi>c</mml:mi><mml:mi mathvariant="normal">P</mml:mi></mml:msubsup></mml:mrow></mml:mtd></mml:mlabeledtr></mml:mtable></mml:math></disp-formula>

            and

              <disp-formula id="App1.Ch1.S1.E1.4" content-type="subnumberedoff"><label>A1c</label><mml:math id="M225" display="block"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mi>a</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mi>a</mml:mi><mml:mi mathvariant="normal">O</mml:mi></mml:msubsup><mml:mo>-</mml:mo><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mi>a</mml:mi><mml:mi mathvariant="normal">P</mml:mi></mml:msubsup><mml:mo>=</mml:mo><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mi>f</mml:mi><mml:mi mathvariant="normal">O</mml:mi></mml:msubsup><mml:mo>+</mml:mo><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mi>c</mml:mi><mml:mi mathvariant="normal">O</mml:mi></mml:msubsup><mml:mo>-</mml:mo><mml:mfenced open="(" close=")"><mml:mrow><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mi>f</mml:mi><mml:mi mathvariant="normal">P</mml:mi></mml:msubsup><mml:mo>+</mml:mo><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mi>c</mml:mi><mml:mi mathvariant="normal">P</mml:mi></mml:msubsup></mml:mrow></mml:mfenced><mml:mo>=</mml:mo><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mi>f</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mi>c</mml:mi></mml:msub><mml:mspace width="0.33em" linebreak="nobreak"/></mml:mrow></mml:math></disp-formula></p>
</sec>
<sec id="App1.Ch1.S1.SS1.SSS2">
  <label>A1.2</label><title>Temporal resampling considerations for the two CIMELs and the lidar</title>
      <p id="d2e3860"><list list-type="custom">
              <list-item><label>1.</label>

      <p id="d2e3865"><inline-formula><mml:math id="M226" display="inline"><mml:mrow><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mi>c</mml:mi><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>,</mml:mo><mml:mi mathvariant="normal">O</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:math></inline-formula> represents <inline-formula><mml:math id="M227" display="inline"><mml:mrow><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mi>c</mml:mi><mml:mi>l</mml:mi></mml:msubsup></mml:mrow></mml:math></inline-formula> resampled to <inline-formula><mml:math id="M228" display="inline"><mml:mrow><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mi>c</mml:mi><mml:mi mathvariant="normal">O</mml:mi></mml:msubsup></mml:mrow></mml:math></inline-formula> times while we use <inline-formula><mml:math id="M229" display="inline"><mml:mrow><mml:msup><mml:mi>N</mml:mi><mml:mrow><mml:mi>l</mml:mi><mml:mo>,</mml:mo><mml:mi>O</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> to describe the number of resampled points. For the sake of keeping the nomenclature as simple as possible, we dropped the “O” superscript from <inline-formula><mml:math id="M230" display="inline"><mml:mrow><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mi>c</mml:mi><mml:mrow><mml:mi>l</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">O</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:math></inline-formula> (i.e. there is only one lidar).</p>
              </list-item>
              <list-item><label>2.</label>

      <p id="d2e3948"><inline-formula><mml:math id="M231" display="inline"><mml:mrow><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mi>c</mml:mi><mml:mrow><mml:mi mathvariant="normal">P</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">O</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:math></inline-formula> represents <inline-formula><mml:math id="M232" display="inline"><mml:mrow><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mi>c</mml:mi><mml:mi mathvariant="normal">P</mml:mi></mml:msubsup></mml:mrow></mml:math></inline-formula> resampled to <inline-formula><mml:math id="M233" display="inline"><mml:mrow><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mi>c</mml:mi><mml:mi mathvariant="normal">O</mml:mi></mml:msubsup></mml:mrow></mml:math></inline-formula> times<fn id="App1.Ch1.Footn1"><p id="d2e3994">but <inline-formula><mml:math id="M234" display="inline"><mml:mrow><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mi>c</mml:mi><mml:mi mathvariant="normal">P</mml:mi></mml:msubsup></mml:mrow></mml:math></inline-formula> is shown in the PowerPoint profiles</p></fn> while using <inline-formula><mml:math id="M235" display="inline"><mml:mrow><mml:msup><mml:mi>N</mml:mi><mml:mrow><mml:mi mathvariant="normal">P</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">O</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> to represent the number of resampled points. <inline-formula><mml:math id="M236" display="inline"><mml:mrow><mml:msup><mml:mi>N</mml:mi><mml:mrow><mml:mi mathvariant="normal">P</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">O</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M237" display="inline"><mml:mo>≠</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M238" display="inline"><mml:mrow><mml:msup><mml:mi>N</mml:mi><mml:mrow><mml:mi>l</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">O</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> if, for example, the PEARL measurements are limited in temporal extent relative to the 0PAL temporal extent.</p>
              </list-item>
              <list-item><label>3.</label>

      <p id="d2e4070">Accordingly, <inline-formula><mml:math id="M239" display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mi>c</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is more precisely defined as <inline-formula><mml:math id="M240" display="inline"><mml:mrow><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mi>c</mml:mi><mml:mi mathvariant="normal">O</mml:mi></mml:msubsup></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M241" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M242" display="inline"><mml:mrow><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mi>c</mml:mi><mml:mrow><mml:mi mathvariant="normal">P</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">O</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:math></inline-formula>. We employ <inline-formula><mml:math id="M243" display="inline"><mml:mrow><mml:msup><mml:mi>N</mml:mi><mml:mi mathvariant="normal">O</mml:mi></mml:msup></mml:mrow></mml:math></inline-formula> to represent the common lidar and PEARL resample points <inline-formula><mml:math id="M244" display="inline"><mml:mrow><mml:mo>(</mml:mo><mml:msup><mml:mi>N</mml:mi><mml:mi mathvariant="normal">O</mml:mi></mml:msup></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M245" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M246" display="inline"><mml:mrow><mml:msup><mml:mi>N</mml:mi><mml:mrow><mml:mi>l</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">O</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M247" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M248" display="inline"><mml:mrow><mml:msup><mml:mi>N</mml:mi><mml:mrow><mml:mi mathvariant="normal">P</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">O</mml:mi></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>.</p>
              </list-item>
            </list>The resampling applied to estimate <inline-formula><mml:math id="M249" display="inline"><mml:mrow><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mi>c</mml:mi><mml:mi>l</mml:mi></mml:msubsup></mml:mrow></mml:math></inline-formula> or <inline-formula><mml:math id="M250" display="inline"><mml:mrow><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mi>c</mml:mi><mml:mrow><mml:mi mathvariant="normal">P</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">O</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:math></inline-formula> was respectively nearest neighbour<fn id="App1.Ch1.Footn2"><p id="d2e4231">the value of <inline-formula><mml:math id="M251" display="inline"><mml:mrow><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mi>c</mml:mi><mml:mi>l</mml:mi></mml:msubsup></mml:mrow></mml:math></inline-formula> at the nominal <inline-formula><mml:math id="M252" display="inline"><mml:mrow><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mi>c</mml:mi><mml:mi>l</mml:mi></mml:msubsup></mml:mrow></mml:math></inline-formula> time contained within a particular 0PAL (1 min) time bin (where the general AERONET sampling frequency is every 3 min: see Giles et al., 2019 for details on CIMEL sampling),</p></fn> and linear  interpolation<fn id="App1.Ch1.Footn3"><p id="d2e4261">between the two <inline-formula><mml:math id="M253" display="inline"><mml:mrow><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mi>c</mml:mi><mml:mi mathvariant="normal">P</mml:mi></mml:msubsup></mml:mrow></mml:math></inline-formula> values at the two nominal PEARL times on either side of a particular <inline-formula><mml:math id="M254" display="inline"><mml:mrow><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mi>c</mml:mi><mml:mi mathvariant="normal">O</mml:mi></mml:msubsup></mml:mrow></mml:math></inline-formula> time</p></fn></p>

      <fig id="FA1"><label>Figure A1</label><caption><p id="d2e4292">Computed variation of the 532 nm DR as a function of effective radius (top horizontal scale) and various assumed ice particle shapes (Fig. 1 of Mishchenko and Sassen, 1998). Optically significant, column-integrated FM particles are largely contained within a radius range of 0.1 to 0.2 <inline-formula><mml:math id="M255" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula> (indicated by the red-dotted vertical lines which we appended to the original figure). This demonstrates that the PDR of FM particles is <inline-formula><mml:math id="M256" display="inline"><mml:mrow><mml:mo>&lt;</mml:mo><mml:mo>∼</mml:mo></mml:mrow></mml:math></inline-formula> a few % for all particle shapes considered by the authors.</p></caption>
            
            <graphic xlink:href="https://amt.copernicus.org/articles/19/4553/2026/amt-19-4553-2026-f10.png"/>

          </fig>

</sec>
</sec>
<sec id="App1.Ch1.S1.SS2">
  <label>A2</label><title>FM and CM attributions for the AHSRL lidar</title>
      <p id="d2e4332">If the FM and CM PDR (particle depolarization ratio<fn id="App1.Ch1.Footn4"><p id="d2e4335">PDR is a common (intensive-parameter) label for that is typically (if rather simplistically) associated with a given type of atmospheric particle. See, for example, Liu et al. (2013)</p></fn>) candidates are defined by holistic FM and CM PDR distributions (whose size-averaged PDRs are <inline-formula><mml:math id="M257" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">δ</mml:mi><mml:mi>f</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M258" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">δ</mml:mi><mml:mi>c</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) then the optically weighted average VDR can be written as;
          

            <disp-formula id="App1.Ch1.S1.E5.6" content-type="subnumberedon"><label>A2a</label><mml:math id="M259" display="block"><mml:mrow><mml:mtext>VDR</mml:mtext><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msub><mml:mi mathvariant="italic">δ</mml:mi><mml:mi>f</mml:mi></mml:msub><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow><mml:mi mathvariant="italic">β</mml:mi><mml:mo>,</mml:mo><mml:mi>f</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi mathvariant="italic">δ</mml:mi><mml:mi>c</mml:mi></mml:msub><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow><mml:mi mathvariant="italic">β</mml:mi><mml:mo>,</mml:mo><mml:mi>c</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow><mml:mi mathvariant="italic">β</mml:mi><mml:mo>,</mml:mo><mml:mi>f</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow><mml:mi mathvariant="italic">β</mml:mi><mml:mo>,</mml:mo><mml:mi>c</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>

          where FM and CM (lidar profile) pixels can be defined, respectively by <inline-formula><mml:math id="M260" display="inline"><mml:mi mathvariant="italic">δ</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M261" display="inline"><mml:mo>≤</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M262" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">δ</mml:mi><mml:mi mathvariant="normal">thr</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M263" display="inline"><mml:mi mathvariant="italic">δ</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M264" display="inline"><mml:mo>&gt;</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M265" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">δ</mml:mi><mml:mi mathvariant="normal">thr</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> if there is a <inline-formula><mml:math id="M266" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">δ</mml:mi><mml:mi mathvariant="normal">thr</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> saddle between the PDRs.

                <disp-formula specific-use="gather" content-type="numbered"><mml:math id="M267" display="block"><mml:mtable displaystyle="true"><mml:mlabeledtr id="App1.Ch1.S1.E5.7"><mml:mtd><mml:mtext>A2b</mml:mtext></mml:mtd><mml:mtd><mml:mrow><mml:mstyle displaystyle="true" class="stylechange"/><mml:mo>=</mml:mo><mml:msub><mml:mi mathvariant="italic">δ</mml:mi><mml:mi>f</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">η</mml:mi><mml:mrow><mml:mi mathvariant="italic">β</mml:mi><mml:mo>,</mml:mo><mml:mi>c</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfenced><mml:mo>+</mml:mo><mml:msub><mml:mi mathvariant="italic">δ</mml:mi><mml:mi>c</mml:mi></mml:msub><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msub><mml:mi mathvariant="italic">η</mml:mi><mml:mrow><mml:mi mathvariant="italic">β</mml:mi><mml:mo>,</mml:mo><mml:mi>c</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mlabeledtr><mml:mlabeledtr id="App1.Ch1.S1.E5.8"><mml:mtd><mml:mtext>A2c</mml:mtext></mml:mtd><mml:mtd><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><mml:mo>=</mml:mo><mml:msub><mml:mi mathvariant="italic">δ</mml:mi><mml:mi>f</mml:mi></mml:msub><mml:msub><mml:mi mathvariant="italic">η</mml:mi><mml:mrow><mml:mi mathvariant="italic">β</mml:mi><mml:mo>,</mml:mo><mml:mi>f</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi mathvariant="italic">δ</mml:mi><mml:mi>c</mml:mi></mml:msub><mml:mfenced open="(" close=")"><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>-</mml:mo><mml:msub><mml:mi mathvariant="italic">η</mml:mi><mml:mrow><mml:mi mathvariant="italic">β</mml:mi><mml:mo>,</mml:mo><mml:mi>f</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfenced><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mlabeledtr></mml:mtable></mml:math></disp-formula>

          where we define

            <disp-formula id="App1.Ch1.S1.E5.9" content-type="subnumberedoff"><label>A2d</label><mml:math id="M268" display="block"><mml:mrow><mml:msub><mml:mi mathvariant="italic">η</mml:mi><mml:mrow><mml:mi mathvariant="italic">β</mml:mi><mml:mo>,</mml:mo><mml:mi>c</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow><mml:mi mathvariant="italic">β</mml:mi><mml:mo>,</mml:mo><mml:mi>c</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow><mml:mi mathvariant="italic">β</mml:mi><mml:mo>,</mml:mo><mml:mi>c</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow><mml:mi mathvariant="italic">β</mml:mi><mml:mo>,</mml:mo><mml:mi>f</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:mspace width="0.25em" linebreak="nobreak"/><mml:mspace linebreak="nobreak" width="0.25em"/><mml:mtext>and</mml:mtext><mml:mspace linebreak="nobreak" width="0.25em"/><mml:mspace linebreak="nobreak" width="0.25em"/><mml:msub><mml:mi mathvariant="italic">η</mml:mi><mml:mrow><mml:mi mathvariant="italic">β</mml:mi><mml:mo>,</mml:mo><mml:mi>f</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow><mml:mi mathvariant="italic">β</mml:mi><mml:mo>,</mml:mo><mml:mi>f</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow><mml:mi mathvariant="italic">β</mml:mi><mml:mo>,</mml:mo><mml:mi>c</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow><mml:mi mathvariant="italic">β</mml:mi><mml:mo>,</mml:mo><mml:mi>f</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>=</mml:mo><mml:mfenced open="(" close=")"><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>-</mml:mo><mml:msub><mml:mi mathvariant="italic">η</mml:mi><mml:mrow><mml:mi mathvariant="italic">β</mml:mi><mml:mo>,</mml:mo><mml:mi>c</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfenced></mml:mrow></mml:math></disp-formula>

          As we will argue below, the lidar optical depths (<inline-formula><mml:math id="M269" display="inline"><mml:mrow><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mi>c</mml:mi><mml:mi>l</mml:mi></mml:msubsup></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M270" display="inline"><mml:mrow><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mi>f</mml:mi><mml:mi>l</mml:mi></mml:msubsup></mml:mrow></mml:math></inline-formula> in the main text<fn id="App1.Ch1.Footn5"><p id="d2e4756">where <inline-formula><mml:math id="M271" display="inline"><mml:mrow><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mi>c</mml:mi><mml:mi>l</mml:mi></mml:msubsup></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M272" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M273" display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi>c</mml:mi></mml:msub><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow><mml:mi mathvariant="italic">β</mml:mi><mml:mo>,</mml:mo><mml:mi>c</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M274" display="inline"><mml:mrow><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mi>f</mml:mi><mml:mi>l</mml:mi></mml:msubsup></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M275" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M276" display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi>f</mml:mi></mml:msub><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow><mml:mi mathvariant="italic">β</mml:mi><mml:mo>,</mml:mo><mml:mi>f</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> (<inline-formula><mml:math id="M277" display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi>c</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M278" display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi>f</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> being their respective lidar ratios)</p></fn>) can provide reasonable estimates of <inline-formula><mml:math id="M279" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mi>c</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M280" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mi>f</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> for a strategic choice of <inline-formula><mml:math id="M281" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">δ</mml:mi><mml:mi mathvariant="normal">thr</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>. If the FM and CM PDRs are defined in a binary fashion by a <inline-formula><mml:math id="M282" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">δ</mml:mi><mml:mi mathvariant="normal">thr</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> threshold then those PDRs can be written,
          

                <disp-formula id="App1.Ch1.S1.E10" specific-use="gather" content-type="subnumberedsingle"><mml:math id="M283" display="block"><mml:mtable displaystyle="true"><mml:mlabeledtr id="App1.Ch1.S1.E10.11"><mml:mtd><mml:mtext>A3a</mml:mtext></mml:mtd><mml:mtd><mml:mrow><mml:mstyle displaystyle="true" class="stylechange"/><mml:msubsup><mml:mi mathvariant="italic">δ</mml:mi><mml:mi>f</mml:mi><mml:mo>′</mml:mo></mml:msubsup><mml:mo>=</mml:mo><mml:mo>〈</mml:mo><mml:msup><mml:mtext>VDR</mml:mtext><mml:mrow><mml:mi mathvariant="italic">δ</mml:mi><mml:mo>≤</mml:mo><mml:msub><mml:mi mathvariant="italic">δ</mml:mi><mml:mi mathvariant="normal">thr</mml:mi></mml:msub></mml:mrow></mml:msup><mml:mo>〉</mml:mo></mml:mrow></mml:mtd></mml:mlabeledtr><mml:mlabeledtr id="App1.Ch1.S1.E10.12"><mml:mtd><mml:mtext>A3b</mml:mtext></mml:mtd><mml:mtd><mml:mrow><mml:mstyle displaystyle="true" class="stylechange"/><mml:msubsup><mml:mi mathvariant="italic">δ</mml:mi><mml:mi>c</mml:mi><mml:mo>′</mml:mo></mml:msubsup><mml:mo>=</mml:mo><mml:mo>〈</mml:mo><mml:msup><mml:mtext>VDR</mml:mtext><mml:mrow><mml:mi mathvariant="italic">δ</mml:mi><mml:mo>&gt;</mml:mo><mml:msub><mml:mi mathvariant="italic">δ</mml:mi><mml:mi mathvariant="normal">thr</mml:mi></mml:msub></mml:mrow></mml:msup><mml:mo>〉</mml:mo></mml:mrow></mml:mtd></mml:mlabeledtr></mml:mtable></mml:math></disp-formula>

          The “<inline-formula><mml:math id="M284" display="inline"><mml:mrow><mml:mo>〈</mml:mo><mml:mtext>VDR</mml:mtext><mml:mo>〉</mml:mo></mml:mrow></mml:math></inline-formula>” symbolism represents some weighted or unweighted VDR mean in altitude (or in altitude as well as time) where  the <inline-formula><mml:math id="M285" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">δ</mml:mi><mml:mi mathvariant="normal">thr</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>  criterion is applied to every single lidar pixel. Equation (A2) represents a tool for seeking out information about the PDRs of holistic depictions of FM and CM components. One must be wary of the opto-physical differences between <inline-formula><mml:math id="M286" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">δ</mml:mi><mml:mi>f</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M287" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">δ</mml:mi><mml:mi>c</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> versus <inline-formula><mml:math id="M288" display="inline"><mml:mrow><mml:msubsup><mml:mi mathvariant="italic">δ</mml:mi><mml:mi>f</mml:mi><mml:mo>′</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M289" display="inline"><mml:mrow><mml:msubsup><mml:mi mathvariant="italic">δ</mml:mi><mml:mi>c</mml:mi><mml:mo>′</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula> respectively<fn id="App1.Ch1.Footn6"><p id="d2e5061">Equation (A2) represents a continuously varying function of <inline-formula><mml:math id="M290" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">η</mml:mi><mml:mi>c</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> or <inline-formula><mml:math id="M291" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">η</mml:mi><mml:mi>f</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> while Eq. (A3) is a step function of <inline-formula><mml:math id="M292" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">δ</mml:mi><mml:mi mathvariant="normal">thr</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> (stepping from <inline-formula><mml:math id="M293" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">δ</mml:mi><mml:mi mathvariant="normal">thr</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>-dependent values of <inline-formula><mml:math id="M294" display="inline"><mml:mrow><mml:mo>〈</mml:mo><mml:mtext>VDR</mml:mtext><mml:mo>〉</mml:mo></mml:mrow></mml:math></inline-formula> for <inline-formula><mml:math id="M295" display="inline"><mml:mrow><mml:mi mathvariant="italic">δ</mml:mi><mml:mo>≤</mml:mo><mml:msub><mml:mi mathvariant="italic">δ</mml:mi><mml:mi mathvariant="normal">thr</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> to <inline-formula><mml:math id="M296" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">δ</mml:mi><mml:mi mathvariant="normal">thr</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>-dependent values of <inline-formula><mml:math id="M297" display="inline"><mml:mrow><mml:mo>〈</mml:mo><mml:mtext>VDR</mml:mtext><mml:mo>〉</mml:mo></mml:mrow></mml:math></inline-formula> for <inline-formula><mml:math id="M298" display="inline"><mml:mrow><mml:mi mathvariant="italic">δ</mml:mi><mml:mo>&gt;</mml:mo><mml:msub><mml:mi mathvariant="italic">δ</mml:mi><mml:mi mathvariant="normal">thr</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>)</p></fn> and their link with the measured VDR (or averages of measured VDRs). The two formulations can be investigated by varying <inline-formula><mml:math id="M299" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">δ</mml:mi><mml:mi mathvariant="normal">thr</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> until some optimal solution is obtained for any given event. Part of the process is the recognition that <inline-formula><mml:math id="M300" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">δ</mml:mi><mml:mi>f</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is known (empirically and theoretically) to be small (<inline-formula><mml:math id="M301" display="inline"><mml:mrow><mml:mo>&lt;</mml:mo><mml:mo>∼</mml:mo></mml:mrow></mml:math></inline-formula> a few %; see Fig. A1 for example) while <inline-formula><mml:math id="M302" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">δ</mml:mi><mml:mi>c</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> of dust particles generally increases with increasing <inline-formula><mml:math id="M303" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">δ</mml:mi><mml:mi mathvariant="normal">thr</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> in the range where dust-particle population is significant<fn id="App1.Ch1.Footn7"><p id="d2e5230">Where the particle volume sized distribution is significant: see, e.g., Mamouri and Ansmann, 2014 (MA)</p></fn>. We suppose that the PDR of other particulate species (clouds, for example) are easily separable from our FM and CM aerosol species.</p>
</sec>
<sec id="App1.Ch1.S1.SS3">
  <label>A3</label><title>The need for vertically-averaged VDR weighting</title>
      <p id="d2e5242">AHSRL <inline-formula><mml:math id="M304" display="inline"><mml:mi mathvariant="italic">β</mml:mi></mml:math></inline-formula> and VDR profiles (along with derived values of lidar, 0PAL and PEARL CM AODs) for the 7 Eureka dust events that we investigated can be observed in the supplementary PowerPoint file “AHSRL_CIMEL_event_profiles”. The VDR values ranged from small-amplitude negative to positive values to large-amplitude negative and positive outliers (see Sect. A3.1 for a detailed discussion of how we processed that data). Dörnbrack et al. (2010) reported on airborne lidar observations and characterization of local dust events over Svalbard in May of 2004. Their results included dust plumes whose VDRs ranged from quite small (<inline-formula><mml:math id="M305" display="inline"><mml:mrow><mml:mo>&lt;</mml:mo><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">5</mml:mn></mml:mrow></mml:math></inline-formula> %) to values larger than 10 % inside the plumes to maximum values of <inline-formula><mml:math id="M306" display="inline"><mml:mrow><mml:mo>&lt;</mml:mo><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">30</mml:mn></mml:mrow></mml:math></inline-formula> % very close to the surface. In the context of the discussion presented in Sect. A2, VDRs of local dust profiles can achieve (extreme FM to CM) values <inline-formula><mml:math id="M307" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 15 %–40 %<fn id="App1.Ch1.Footn8"><p id="d2e5283">See, e.g. MA who argue that their FM and CM dust PDRs [“<inline-formula><mml:math id="M308" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">δ</mml:mi><mml:mrow><mml:mi>d</mml:mi><mml:mi>f</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>” and “<inline-formula><mml:math id="M309" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">δ</mml:mi><mml:mrow><mml:mi>d</mml:mi><mml:mi>c</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>” respectively] of 16 % and 39 % respectively can generate near-source (Sahara) VDR (<inline-formula><mml:math id="M310" display="inline"><mml:mi mathvariant="italic">δ</mml:mi></mml:math></inline-formula>) values of <inline-formula><mml:math id="M311" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 31 <inline-formula><mml:math id="M312" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 3 % (the values of Freudenthaler et al., 2009 and Grob et al., 2011 as cited in MA).</p></fn>. MA report that their holistic FM component<fn id="App1.Ch1.Footn9"><p id="d2e5337">e.g., the complete (and ubiquitous) FM AERONET-inversion component between <inline-formula><mml:math id="M313" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 0.05 and 0.2 <inline-formula><mml:math id="M314" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula> (radius) seen in their Fig. 4.</p></fn> produces PDRs (<inline-formula><mml:math id="M315" display="inline"><mml:mo lspace="0mm">∼</mml:mo></mml:math></inline-formula> 5 %<fn id="App1.Ch1.Footn10"><p id="d2e5365">for what they call “non-dust” particles but whose distinctive feature is arguably the limitation to a holistic FM component. See also, for example, the precipitous drop in simulated <inline-formula><mml:math id="M316" display="inline"><mml:mi mathvariant="italic">δ</mml:mi></mml:math></inline-formula> values of ice particles (to magnitudes <inline-formula><mml:math id="M317" display="inline"><mml:mo>&lt;</mml:mo></mml:math></inline-formula> 5 %) for (ice) between the specific cases of 0.05 and 0.2 <inline-formula><mml:math id="M318" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula> radius (effective size parameter between 0.6 and 2.4) in Fig. A1.</p></fn>) while also demonstrating that their sub-<inline-formula><mml:math id="M319" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula> FM dust tail<fn id="App1.Ch1.Footn11"><p id="d2e5403">the tail of what might be called a holistic CM component between <inline-formula><mml:math id="M320" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 0.2 to 10 <inline-formula><mml:math id="M321" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula> radius as seen in their Fig. 4</p></fn> can induce a significant VDR increase relative to the holistic FM component<fn id="App1.Ch1.Footn12"><p id="d2e5424">MA's AERONET PSD shows a not insignificant (sub-<inline-formula><mml:math id="M322" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula>) FM tail of that CM component. It is this tail that surely drives their FM (“<inline-formula><mml:math id="M323" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">δ</mml:mi><mml:mrow><mml:mi>d</mml:mi><mml:mi>f</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>”) estimate of 16 %.</p></fn> and that super-<inline-formula><mml:math id="M324" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula> particles can induce even larger VDRs. See Fig. 3a and b above for empirical examples showing a super-<inline-formula><mml:math id="M325" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula> CM peak radius at our 0PAL site (after the advent of the stronger dust event at 20:30 UTC).</p>
<sec id="App1.Ch1.S1.SS3.SSS1">
  <label>A3.1</label><title>VDR weighting options</title>
      <p id="d2e5480">VDR profile averages (<inline-formula><mml:math id="M326" display="inline"><mml:mrow><mml:mo>〈</mml:mo><mml:mtext>VDR</mml:mtext><mml:mo>〉</mml:mo></mml:mrow></mml:math></inline-formula>) between 82 and 615 m<fn id="App1.Ch1.Footn13"><p id="d2e5495">the difference in elevation between 0PAL and PEARL (except that the 82.5 m is above the 0PAL elevation of 5 m). The statistics start at 82.5 m because the VDR below 82.5 m was judged to be too noisy.</p></fn> were found, in the initial processing run, to be systematically too large<fn id="App1.Ch1.Footn14"><p id="d2e5499">too many values well above the typical VDR range for CM dust (see, for example, Fig. 1 of Tian et al., 2020).</p></fn>. This was suspected to be due to the initial choice of not including negative VDR pixels in any given VDR profile average<fn id="App1.Ch1.Footn15"><p id="d2e5503">While retaining the rest of the (positive) VDR pixels in the given profile</p></fn>. Indeed, Fig. A2 shows that the simple removal of negative VDR pixels (blue-colored circles) produced <inline-formula><mml:math id="M327" display="inline"><mml:mrow><mml:mo>〈</mml:mo><mml:mtext>VDR</mml:mtext><mml:mo>〉</mml:mo></mml:mrow></mml:math></inline-formula> estimates that were systematically greater than the two more statistically justifiable methods<fn id="App1.Ch1.Footn16"><p id="d2e5520">Simply put the exclusion of the negative values acted to increase the <inline-formula><mml:math id="M328" display="inline"><mml:mrow><mml:mo>〈</mml:mo><mml:mtext>VDR</mml:mtext><mml:mo>〉</mml:mo></mml:mrow></mml:math></inline-formula> values. This exclusion is debatable given that those negative values could well have a physical sense (they are likely associated with system constants whose range of variability could facilitate the production of negative VDR values for a fraction of the VDRs).</p></fn>. Two alternate methods were investigated to mitigate the impacts of removing negative VDRs : <list list-type="bullet"><list-item>
      <p id="d2e5538"><italic>The 1st method</italic> (green circles) employs no weighting but does not exclude negative VDRs.</p></list-item><list-item>
      <p id="d2e5544"><italic>The 2nd method</italic> includes a weighted mean of all VDRs in any given profile (<inline-formula><mml:math id="M329" display="inline"><mml:mrow><mml:mo>〈</mml:mo><mml:mtext>VDR</mml:mtext><mml:msub><mml:mo>〉</mml:mo><mml:mi mathvariant="italic">ω</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mo>∑</mml:mo><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi mathvariant="italic">ω</mml:mi><mml:mtext>VDR</mml:mtext><mml:mfenced open="/" close=""><mml:mrow><mml:mo>∑</mml:mo><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi mathvariant="italic">ω</mml:mi></mml:mrow></mml:mfenced></mml:mrow></mml:math></inline-formula> where <inline-formula><mml:math id="M330" display="inline"><mml:mi mathvariant="italic">ω</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M331" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M332" display="inline"><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mfenced open="/" close=""><mml:mrow><mml:msup><mml:mtext>RE</mml:mtext><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:mfenced></mml:mrow></mml:math></inline-formula> for each profile pixel<fn id="App1.Ch1.Footn17"><p id="d2e5609">The “RE<sub>RMS</sub>” of the <inline-formula><mml:math id="M334" display="inline"><mml:mi>x</mml:mi></mml:math></inline-formula> axis in Fig. A2 represents the RMS residual error of the individual residual of any lidar pixel in any given vertical profile (the “individual residual” being the difference between a given VDR value at a given altitude and its running average; see the example for two representative lidar profiles in Fig. A3). This RE parameter enables an estimation of the noise magnitude by eliminating the systematic trend of the natural VDR variation. The inverse square weighting approach was inspired by standard texts on linear regression analysis (see, for example, Sect. 3.5 of Barford, 1967)</p></fn>. This takes all VDRs into consideration (does not suffer from the negative-VDR limitations) and seems to produce more realistic <inline-formula><mml:math id="M335" display="inline"><mml:mrow><mml:mo>〈</mml:mo><mml:mtext>VDR</mml:mtext><mml:mo>〉</mml:mo></mml:mrow></mml:math></inline-formula> values than the 1st method (values whose <inline-formula><mml:math id="M336" display="inline"><mml:mrow><mml:mo>〈</mml:mo><mml:mtext>VDR</mml:mtext><mml:mo>〉</mml:mo></mml:mrow></mml:math></inline-formula> range extends less into (both) the negative region and the positive region). Averaging in time (averaging over the event using an optical weighting factor of <inline-formula><mml:math id="M337" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mi mathvariant="italic">β</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) would then be written as;<disp-formula id="App1.Ch1.S1.E13" content-type="numbered"><label>A4</label><mml:math id="M338" display="block"><mml:mrow><mml:mo>〈</mml:mo><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mo>〈</mml:mo><mml:mtext>VDR</mml:mtext><mml:msub><mml:mo>〉</mml:mo><mml:mi mathvariant="italic">ω</mml:mi></mml:msub><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msub><mml:mo>〉</mml:mo><mml:mrow><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mi mathvariant="italic">β</mml:mi></mml:msub></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mo movablelimits="false">∑</mml:mo><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mo>〈</mml:mo><mml:mtext>VDR</mml:mtext><mml:msub><mml:mo>〉</mml:mo><mml:mi mathvariant="italic">ω</mml:mi></mml:msub><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mi mathvariant="italic">β</mml:mi></mml:msub><mml:mfenced open="/" close=""><mml:mrow><mml:mo movablelimits="false">∑</mml:mo><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mi mathvariant="italic">β</mml:mi></mml:msub></mml:mrow></mml:mfenced></mml:mrow></mml:math></disp-formula></p></list-item></list></p>

      <fig id="FA2"><label>Figure A2</label><caption><p id="d2e5724">Altitude-averaged VDRs vs RMS residual errors (RE<sub>RMS</sub>) for the 23 July 2007 dust event (the LH graph is a zoom of the RH graph). According to our notation, the orange-colored weighted averages should be labelled <inline-formula><mml:math id="M340" display="inline"><mml:mrow><mml:mo>〈</mml:mo><mml:mtext>VDR</mml:mtext><mml:msub><mml:mo>〉</mml:mo><mml:mi mathvariant="italic">ω</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>. These statistics were computed for the lidar altitude range from 82 to 615 m.</p></caption>
            
            <graphic xlink:href="https://amt.copernicus.org/articles/19/4553/2026/amt-19-4553-2026-f11.png"/>

          </fig>

</sec>
<sec id="App1.Ch1.S1.SS3.SSS2">
  <label>A3.2</label><title>VDR weighting: profile-level impacts and resulting event-averaged statistics</title>
      <p id="d2e5767">The impact of the <inline-formula><mml:math id="M341" display="inline"><mml:mi mathvariant="italic">ω</mml:mi></mml:math></inline-formula> weighting discussed in the previous sections is seen in Figs. S1b to S7b<fn id="App1.Ch1.Footn18"><p id="d2e5777">Supplementary PowerPoint file “AHSRL_CIMEL_event_profiles”</p></fn>. In a nutshell the weighting significantly reduced the intra-profile standard deviations for all events (the bottom graphics of Figs. S1b to S7b). We would also argue that the event-wide average of the intra-profile standard deviation is the best candidate to describe the event-wide precision (noise) of our VDR estimates (see the Fig. S8 caption for details). On the other hand, the weighting introduced a significant amount of VDR variance in 2 events where very little variance existed prior to the weighting process (Events 1 and 6 of Figs. S1b and S6b)<fn id="App1.Ch1.Footn19"><p id="d2e5781">we could have reduced that variance with an appropriate smoothing approach but decided to forgo that added complication by the simple expedient of choosing the unweighted statistics since those statistics were largely free of the type of extreme VDR variation that one sees in the unweighted VDR means of Events 2, 3, 4, 5 and 7.</p></fn>. The Event 1 and 6 standard deviations of intra-profile, event-level statistics that are summarized in the table of Fig. S8 are accordingly to be treated with caution. Indeed, the table shows explicitly that weighting did dramatically reduce the intra-profile standard deviations of all events excluding Events 1 and 6. We accordingly use the intra-profile statistics in the following section on the derivation of the PDRs for each event.</p>
</sec>
<sec id="App1.Ch1.S1.SS3.SSS3">
  <label>A3.3</label><title>Estimation of the event-averaged CM PDR</title>
      <p id="d2e5797">Figure A4 shows the event-averaged VDR and <inline-formula><mml:math id="M342" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mi mathvariant="italic">β</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> values for both the FM and CM components as a function of <inline-formula><mml:math id="M343" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">δ</mml:mi><mml:mi mathvariant="normal">thr</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> (Eq. A3 above<fn id="App1.Ch1.Footn20"><p id="d2e5822">to be mathematically precise, those CM event averages (the <inline-formula><mml:math id="M344" display="inline"><mml:mi>y</mml:mi></mml:math></inline-formula>-axes labels of the LH graphs of Fig. A4) represent <inline-formula><mml:math id="M345" display="inline"><mml:mrow><mml:mo>〈</mml:mo><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mo>〈</mml:mo><mml:msup><mml:mtext>VDR</mml:mtext><mml:mrow><mml:mo>〈</mml:mo><mml:mo>〈</mml:mo><mml:mtext>VDR</mml:mtext><mml:msub><mml:mo>〉</mml:mo><mml:mi mathvariant="italic">ω</mml:mi></mml:msub><mml:msub><mml:mo>〉</mml:mo><mml:mrow><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mi mathvariant="italic">β</mml:mi></mml:msub></mml:mrow></mml:msub><mml:mo>&gt;</mml:mo><mml:msub><mml:mi mathvariant="italic">δ</mml:mi><mml:mi mathvariant="normal">thr</mml:mi></mml:msub></mml:mrow></mml:msup><mml:msub><mml:mo>〉</mml:mo><mml:mi mathvariant="italic">ω</mml:mi></mml:msub><mml:msub><mml:mo>〉</mml:mo><mml:mrow><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mi mathvariant="italic">β</mml:mi></mml:msub></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M346" display="inline"><mml:mrow><mml:mo>〈</mml:mo><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mo>〈</mml:mo><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mi mathvariant="italic">β</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mo>∫</mml:mo><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="italic">β</mml:mi><mml:mrow><mml:mo>〈</mml:mo><mml:mo>〈</mml:mo><mml:mtext>VDR</mml:mtext><mml:msub><mml:mo>〉</mml:mo><mml:mi mathvariant="italic">ω</mml:mi></mml:msub><mml:msub><mml:mo>〉</mml:mo><mml:mrow><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mi mathvariant="italic">β</mml:mi></mml:msub></mml:mrow></mml:msub><mml:mo>&gt;</mml:mo><mml:msub><mml:mi mathvariant="italic">δ</mml:mi><mml:mi mathvariant="normal">thr</mml:mi></mml:msub></mml:mrow></mml:msup><mml:mi mathvariant="normal">d</mml:mi><mml:mi>z</mml:mi></mml:mrow></mml:math></inline-formula> where the VDR vs. <inline-formula><mml:math id="M347" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">δ</mml:mi><mml:mi mathvariant="normal">thr</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> test is applied to each lidar pixel. The RH FM <inline-formula><mml:math id="M348" display="inline"><mml:mi>y</mml:mi></mml:math></inline-formula>-axis labels represent <inline-formula><mml:math id="M349" display="inline"><mml:mrow><mml:mo>〈</mml:mo><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mo>〈</mml:mo><mml:msup><mml:mtext>VDR</mml:mtext><mml:mrow><mml:mo>〈</mml:mo><mml:mo>〈</mml:mo><mml:mtext>VDR</mml:mtext><mml:msub><mml:mo>〉</mml:mo><mml:mi mathvariant="italic">ω</mml:mi></mml:msub><mml:msub><mml:mo>〉</mml:mo><mml:mrow><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mi mathvariant="italic">β</mml:mi></mml:msub></mml:mrow></mml:msub><mml:mo>≤</mml:mo><mml:msub><mml:mi mathvariant="italic">δ</mml:mi><mml:mi mathvariant="normal">thr</mml:mi></mml:msub></mml:mrow></mml:msup><mml:msub><mml:mo>〉</mml:mo><mml:mi mathvariant="italic">ω</mml:mi></mml:msub><mml:msub><mml:mo>〉</mml:mo><mml:mrow><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mi mathvariant="italic">β</mml:mi></mml:msub></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M350" display="inline"><mml:mrow><mml:mo>〈</mml:mo><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mi mathvariant="italic">β</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mo>∫</mml:mo><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="italic">β</mml:mi><mml:mrow><mml:mo>〈</mml:mo><mml:mo>〈</mml:mo><mml:mtext>VDR</mml:mtext><mml:msub><mml:mo>〉</mml:mo><mml:mi mathvariant="italic">ω</mml:mi></mml:msub><mml:msub><mml:mo>〉</mml:mo><mml:mrow><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mi mathvariant="italic">β</mml:mi></mml:msub></mml:mrow></mml:msub><mml:mo>≤</mml:mo><mml:msub><mml:mi mathvariant="italic">δ</mml:mi><mml:mi mathvariant="normal">thr</mml:mi></mml:msub></mml:mrow></mml:msup><mml:mi mathvariant="normal">d</mml:mi><mml:mi>z</mml:mi><mml:mo>〉</mml:mo></mml:mrow></mml:math></inline-formula></p></fn>). The CM event averages are rather insensitive to small values of <inline-formula><mml:math id="M351" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">δ</mml:mi><mml:mi mathvariant="normal">thr</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> (arguably because the weak PDR of the FM component and perhaps the weak DR of the sub-<inline-formula><mml:math id="M352" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula> tail of the holistic CM PDR have little impact at small values of <inline-formula><mml:math id="M353" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">δ</mml:mi><mml:mi mathvariant="normal">thr</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>). They only begin to rise when, we would argue, the sub-<inline-formula><mml:math id="M354" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula> tail begins to play a more significant optical role (the larger DR of the sub-<inline-formula><mml:math id="M355" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula> tail incites the beginning of a positive slope that starts to rise at <inline-formula><mml:math id="M356" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">δ</mml:mi><mml:mi mathvariant="normal">thr</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> values ranging from 5 % to 15 %. A stable estimate of the dust PDR would occur at any value before the rises begin, say at <inline-formula><mml:math id="M357" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">δ</mml:mi><mml:mi mathvariant="normal">thr</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M358" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 5 %</p><fig id="FA3"><label>Figure A3</label><caption><p id="d2e6158">Two representative lidar profiles (solid-shaded circles), their running mean (dotted curve) and their residual error (RE) difference (dashed curve).</p></caption>
            
            <graphic xlink:href="https://amt.copernicus.org/articles/19/4553/2026/amt-19-4553-2026-f12.png"/>

          </fig>

      <p id="d2e6169">That 5 % value was chosen to populate the event-dependent 532 nm PDR values of Table A1. Two of the Table A1 values are beyond the (780 nm) VDR upper limit for CM dust found, for example, in Fig. 1 of Tian et al. (2020, their upper limit was <inline-formula><mml:math id="M359" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 50 % for dust particles ranging in radius from <inline-formula><mml:math id="M360" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 1 to 5 <inline-formula><mml:math id="M361" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula><fn id="App1.Ch1.Footn21"><p id="d2e6195">Values which would tend to be moderately larger at 532 nm (see, for example, Table 1 of Mamouri and Ansmann, 2017).</p></fn>). On the other hand, all the Table A1 PDR values are largely contained within the 532 nm lidar ratio spread of “giant” near-source Saharan dust particles reported by Esselborn et al. (2009): their Fig. 9 lidar ratios vary between 40 and 60 sr for dust particles of volume median radii ranging from 4 to 15 <inline-formula><mml:math id="M362" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula> (a spread that encompasses the 7 <inline-formula><mml:math id="M363" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula> radius AERONET inversion dust peak that we report above in Fig. 3a). It should be emphasized that choices such as the (“<inline-formula><mml:math id="M364" display="inline"><mml:mi mathvariant="italic">ω</mml:mi></mml:math></inline-formula>”) weighting scheme and the optimal <inline-formula><mml:math id="M365" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">δ</mml:mi><mml:mi mathvariant="normal">thr</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> value contain a level of subjective variability (in terms of, for example, the strengths of the weights applied). These factors and other sources of variability produce uncertainties that we estimate as being <inline-formula><mml:math id="M366" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M367" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> the “<inline-formula><mml:math id="M368" display="inline"><mml:mi mathvariant="italic">σ</mml:mi></mml:math></inline-formula>(PDR)” values of Table A1.</p><fig id="FA4"><label>Figure A4</label><caption><p id="d2e6267">VDR averaged results as a function of <inline-formula><mml:math id="M369" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">δ</mml:mi><mml:mi mathvariant="normal">thr</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> for our 7 dust events. LH graphs (CM; the CM component of the “binary” model defined in Sect. A2 above; for VDR values <inline-formula><mml:math id="M370" display="inline"><mml:mo>&gt;</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M371" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">δ</mml:mi><mml:mi mathvariant="normal">thr</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>): <bold>(a)</bold> Altitude- and event-averaged VDR<sub><italic>c</italic></sub> values, <bold>(b)</bold> <inline-formula><mml:math id="M373" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow><mml:mi mathvariant="italic">β</mml:mi><mml:mo>,</mml:mo><mml:mi>c</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> values with offset correction and <bold>(c)</bold> <inline-formula><mml:math id="M374" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow><mml:mi mathvariant="italic">β</mml:mi><mml:mo>,</mml:mo><mml:mi>c</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> with no offset correction. RH graphs <bold>(d, e, f)</bold>: the same array of graphs as the left-hand side but for the FM (VDR values <inline-formula><mml:math id="M375" display="inline"><mml:mo>≤</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M376" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">δ</mml:mi><mml:mi mathvariant="normal">thr</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>). The “offset correction” was a constant offset added on to <inline-formula><mml:math id="M377" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">β</mml:mi><mml:mi>c</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M378" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">β</mml:mi><mml:mi>f</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> values to eliminate weakly negative <inline-formula><mml:math id="M379" display="inline"><mml:mi mathvariant="italic">β</mml:mi></mml:math></inline-formula> values (due, we presume, to a small calibration inconsistancy). The “Lower limit” and “Upper limit” are roughly-estimated expected bounds (the extremes of 0PAL values of <inline-formula><mml:math id="M380" display="inline"><mml:mrow><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mi>f</mml:mi><mml:mi mathvariant="normal">O</mml:mi></mml:msubsup></mml:mrow></mml:math></inline-formula> computed for each event using a Eureka (experience-based) estimate of the optically active FM lidar backscatter region (<inline-formula><mml:math id="M381" display="inline"><mml:mo lspace="0mm">∼</mml:mo></mml:math></inline-formula> 5 to 11 km) and the 0.615 km value of L (the atmospheric layer between 0PAL and PEARL)) on <inline-formula><mml:math id="M382" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow><mml:mi mathvariant="italic">β</mml:mi><mml:mo>,</mml:mo><mml:mi>f</mml:mi></mml:mrow></mml:msub><mml:mo>(</mml:mo><mml:mn mathvariant="normal">0</mml:mn><mml:mo>,</mml:mo><mml:mi mathvariant="normal">L</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> (the FM backscatter optical depth across L). These statistics were computed for the lidar altitude range from 7.5 to 615 m (a more extensive range than that which was reported in the legend of Fig. A2; tests showed that the averaged VDR values were very similar in the face of such small changes in the profile range).</p></caption>
            
            <graphic xlink:href="https://amt.copernicus.org/articles/19/4553/2026/amt-19-4553-2026-f13.png"/>

          </fig>

      <p id="d2e6456">The FM VDR averages are significantly more sensitive to <inline-formula><mml:math id="M383" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">δ</mml:mi><mml:mi mathvariant="normal">thr</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> changes at smaller values of that parameter. This is due to a combination of relatively small numbers of VDR pixels being available at small <inline-formula><mml:math id="M384" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">δ</mml:mi><mml:mi mathvariant="normal">thr</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> values and the fact that there seemed  to be a small negative  bias in the <inline-formula><mml:math id="M385" display="inline"><mml:mi mathvariant="italic">β</mml:mi></mml:math></inline-formula>  values. The  <inline-formula><mml:math id="M386" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mi mathvariant="italic">β</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> weighting across each event then produces wildly oscillating VDR averages at <inline-formula><mml:math id="M387" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">δ</mml:mi><mml:mi mathvariant="normal">thr</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> values of 5 % and 10 % (Event 2, 3, 4, 5 and 7 cases of Fig. A4d) that were enhanced by the very small <inline-formula><mml:math id="M388" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mi mathvariant="italic">β</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> weights in the denominator of the weighting expression. The small negative bias was the cause of unrealistically small <inline-formula><mml:math id="M389" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow><mml:mi mathvariant="italic">β</mml:mi><mml:mo>,</mml:mo><mml:mi>f</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> values for the <inline-formula><mml:math id="M390" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">δ</mml:mi><mml:mi mathvariant="normal">thr</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M391" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 5 % case in Fig. A4f. Adding a small <inline-formula><mml:math id="M392" display="inline"><mml:mi mathvariant="italic">β</mml:mi></mml:math></inline-formula> offset to all the <inline-formula><mml:math id="M393" display="inline"><mml:mi mathvariant="italic">β</mml:mi></mml:math></inline-formula> values produced the more realistic “Offset correction” values of Fig. A4f (values that fit into a range of expected <inline-formula><mml:math id="M394" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow><mml:mi mathvariant="italic">β</mml:mi><mml:mo>,</mml:mo><mml:mi>f</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> values between the horizontal dotted lines; see the caption of Fig. A4 for further details).</p>

<table-wrap id="TA1"><label>Table A1</label><caption><p id="d2e6594">Dust PDRs for our 7 dust events (<inline-formula><mml:math id="M395" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">δ</mml:mi><mml:mi mathvariant="normal">thr</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M396" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 5 %). The event colors are consistent with Fig. A4. The precision estimates are event-averaged, intra profile standard deviations discussed in Sect. A3.2</p></caption>
  <graphic xlink:href="https://amt.copernicus.org/articles/19/4553/2026/amt-19-4553-2026-t02-part01.png"/>
</table-wrap>

</sec>
</sec>
<sec id="App1.Ch1.S1.SS4">
  <label>A4</label><title>Does it help to perform a (<inline-formula><mml:math id="M397" display="inline"><mml:mi mathvariant="italic">ω</mml:mi></mml:math></inline-formula>) weighted CM and FM classification?</title>
      <p id="d2e6637">If the VDR is so noisy that it requires weighting in the production of altitude-averaged VDRs then the question arises as to the variability of the VDR-dependent classification of CM and FM aerosols. An approach, which is arguably coherent with our VDR (residual error) weighting scheme, is to associate the VDR weights (which could be thought of as a “number of virtual pixels” that increase the importance attributed to a given lidar pixel). Our unweighted FM/CM backscatter AOD separation is, for the <inline-formula><mml:math id="M398" display="inline"><mml:mi>J</mml:mi></mml:math></inline-formula>th lidar-profile at time <inline-formula><mml:math id="M399" display="inline"><mml:mrow><mml:msub><mml:mi>t</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>J</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>;

            <disp-formula id="App1.Ch1.S1.E14" content-type="numbered"><label>A5</label><mml:math id="M400" display="block"><mml:mtable class="split" rowspacing="0.2ex" displaystyle="true" columnalign="right left"><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow><mml:mi mathvariant="italic">β</mml:mi><mml:mi>c</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mfenced open="(" close=")"><mml:mrow><mml:msub><mml:mo>∑</mml:mo><mml:mi>i</mml:mi></mml:msub><mml:msubsup><mml:mi mathvariant="italic">β</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>J</mml:mi></mml:mrow><mml:mrow><mml:msub><mml:mi mathvariant="normal">VDR</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>J</mml:mi></mml:mrow></mml:msub><mml:mo>≥</mml:mo><mml:msub><mml:mi mathvariant="italic">δ</mml:mi><mml:mi mathvariant="normal">thr</mml:mi></mml:msub></mml:mrow></mml:msubsup></mml:mrow></mml:mfenced><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>z</mml:mi><mml:mspace linebreak="nobreak" width="0.25em"/><mml:mspace linebreak="nobreak" width="0.25em"/><mml:mtext>and</mml:mtext></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow><mml:mi mathvariant="italic">β</mml:mi><mml:mi>f</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mfenced open="(" close=")"><mml:mrow><mml:msub><mml:mo>∑</mml:mo><mml:mi>i</mml:mi></mml:msub><mml:msubsup><mml:mi mathvariant="italic">β</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>J</mml:mi></mml:mrow><mml:mrow><mml:msub><mml:mi mathvariant="normal">VDR</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>J</mml:mi></mml:mrow></mml:msub><mml:mo>&lt;</mml:mo><mml:msub><mml:mi mathvariant="italic">δ</mml:mi><mml:mi mathvariant="normal">thr</mml:mi></mml:msub></mml:mrow></mml:msubsup></mml:mrow></mml:mfenced><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>z</mml:mi><mml:mspace linebreak="nobreak" width="0.25em"/><mml:mspace width="0.25em" linebreak="nobreak"/><mml:mtext>where</mml:mtext><mml:mspace linebreak="nobreak" width="0.25em"/><mml:mspace width="0.25em" linebreak="nobreak"/><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow><mml:mi mathvariant="italic">β</mml:mi><mml:mi>c</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow><mml:mi mathvariant="italic">β</mml:mi><mml:mi>f</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mi mathvariant="italic">β</mml:mi></mml:msub></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula>

          This equation explicitly indicates that the <inline-formula><mml:math id="M401" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">β</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>J</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> summations are mutually exclusive and carried out over all altitude bins of a given lidar profile. A weighted version of the FM and CM backscatter ODs for lidar profile <inline-formula><mml:math id="M402" display="inline"><mml:mi>J</mml:mi></mml:math></inline-formula><fn id="App1.Ch1.Footn22"><p id="d2e6833">that takes into account the fact that all parameters (those enclosed in the square brackets) must be restricted by the FM and CM conditions</p></fn>, is<fn id="App1.Ch1.Footn23"><p id="d2e6838">where <inline-formula><mml:math id="M403" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ω</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>J</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> is the <inline-formula><mml:math id="M404" display="inline"><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>/</mml:mo><mml:msup><mml:mtext>RE</mml:mtext><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> weighting defined above</p></fn>,

            <disp-formula id="App1.Ch1.S1.E15" content-type="numbered"><label>A6</label><mml:math id="M405" display="block"><mml:mtable rowspacing="0.2ex" class="split" displaystyle="true" columnalign="right left"><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow><mml:mi mathvariant="italic">β</mml:mi><mml:mi>c</mml:mi></mml:mrow><mml:mi mathvariant="italic">ω</mml:mi></mml:msubsup><mml:mo>=</mml:mo><mml:msub><mml:mi>K</mml:mi><mml:mi>J</mml:mi></mml:msub><mml:msup><mml:mfenced close="]" open="["><mml:mrow><mml:msub><mml:mo>∑</mml:mo><mml:mi>i</mml:mi></mml:msub><mml:msub><mml:mi mathvariant="italic">ω</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>J</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi mathvariant="italic">β</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>J</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfenced><mml:mrow><mml:msub><mml:mi mathvariant="normal">VDR</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>J</mml:mi></mml:mrow></mml:msub><mml:mo>≥</mml:mo><mml:msub><mml:mi mathvariant="italic">δ</mml:mi><mml:mi mathvariant="normal">thr</mml:mi></mml:msub></mml:mrow></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>z</mml:mi><mml:mspace linebreak="nobreak" width="0.25em"/><mml:mspace width="0.25em" linebreak="nobreak"/><mml:mspace width="0.25em" linebreak="nobreak"/><mml:mspace width="0.25em" linebreak="nobreak"/><mml:mtext>and</mml:mtext></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow><mml:mi mathvariant="italic">β</mml:mi><mml:mi>f</mml:mi></mml:mrow><mml:mi mathvariant="italic">ω</mml:mi></mml:msubsup><mml:mo>=</mml:mo><mml:msub><mml:mi>K</mml:mi><mml:mi>J</mml:mi></mml:msub><mml:msup><mml:mfenced open="[" close="]"><mml:mrow><mml:msub><mml:mo>∑</mml:mo><mml:mi>i</mml:mi></mml:msub><mml:msub><mml:mi mathvariant="italic">ω</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>J</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi mathvariant="italic">β</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>J</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfenced><mml:mrow><mml:msub><mml:mi mathvariant="normal">VDR</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>J</mml:mi></mml:mrow></mml:msub><mml:mo>&lt;</mml:mo><mml:msub><mml:mi mathvariant="italic">δ</mml:mi><mml:mi mathvariant="normal">thr</mml:mi></mml:msub></mml:mrow></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>z</mml:mi><mml:mspace linebreak="nobreak" width="0.25em"/><mml:mspace width="0.25em" linebreak="nobreak"/><mml:mspace width="0.25em" linebreak="nobreak"/><mml:mtext>where</mml:mtext></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mi mathvariant="italic">β</mml:mi><mml:mi mathvariant="italic">ω</mml:mi></mml:msubsup><mml:mo>=</mml:mo><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow><mml:mi mathvariant="italic">β</mml:mi><mml:mi>c</mml:mi></mml:mrow><mml:mi mathvariant="italic">ω</mml:mi></mml:msubsup><mml:mo>+</mml:mo><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow><mml:mi mathvariant="italic">β</mml:mi><mml:mi>f</mml:mi></mml:mrow><mml:mi mathvariant="italic">ω</mml:mi></mml:msubsup></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula>

          We then force <inline-formula><mml:math id="M406" display="inline"><mml:mrow><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow><mml:mi mathvariant="italic">β</mml:mi><mml:mi>c</mml:mi></mml:mrow><mml:mi mathvariant="italic">ω</mml:mi></mml:msubsup><mml:mo>+</mml:mo><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow><mml:mi mathvariant="italic">β</mml:mi><mml:mi>f</mml:mi></mml:mrow><mml:mi mathvariant="italic">ω</mml:mi></mml:msubsup></mml:mrow></mml:math></inline-formula> to equal  <inline-formula><mml:math id="M407" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mi mathvariant="italic">β</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> (this simply means that <inline-formula><mml:math id="M408" display="inline"><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mi>J</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is set to <inline-formula><mml:math id="M409" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mi mathvariant="italic">β</mml:mi></mml:msub><mml:mo>/</mml:mo><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mi mathvariant="italic">β</mml:mi><mml:mi mathvariant="italic">ω</mml:mi></mml:msubsup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>. Dividing both sides by <inline-formula><mml:math id="M410" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mi mathvariant="italic">β</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> yields a familiar-looking CMF, FMF (CM fraction, FM fraction) type of relation:
          

            <disp-formula id="App1.Ch1.S1.E16.17" content-type="subnumberedon"><label>A7a</label><mml:math id="M411" display="block"><mml:mrow><mml:msup><mml:mtext>CMF</mml:mtext><mml:mi mathvariant="italic">ω</mml:mi></mml:msup><mml:mo>+</mml:mo><mml:msup><mml:mtext>FMF</mml:mtext><mml:mi mathvariant="italic">ω</mml:mi></mml:msup><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mspace linebreak="nobreak" width="0.25em"/><mml:mspace width="0.25em" linebreak="nobreak"/><mml:mtext>where</mml:mtext></mml:mrow></mml:math></disp-formula>

          (Note that CMF<sup><italic>ω</italic></sup> can be <inline-formula><mml:math id="M413" display="inline"><mml:mo>&gt;</mml:mo></mml:math></inline-formula> 1 if <inline-formula><mml:math id="M414" display="inline"><mml:mrow><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow><mml:mi mathvariant="italic">β</mml:mi><mml:mi>c</mml:mi></mml:mrow><mml:mi mathvariant="italic">ω</mml:mi></mml:msubsup><mml:mo>&gt;</mml:mo><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mi mathvariant="italic">β</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> (negative <inline-formula><mml:math id="M415" display="inline"><mml:mi mathvariant="italic">β</mml:mi></mml:math></inline-formula> values from the real data and attendant underestimates of <inline-formula><mml:math id="M416" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mi mathvariant="italic">β</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> can wreak havoc with the “conservation of unity” equation).)

            <disp-formula id="App1.Ch1.S1.E16.18" content-type="numbered"><label>A7b</label><mml:math id="M417" display="block"><mml:mrow><mml:msup><mml:mtext>CMF</mml:mtext><mml:mi mathvariant="italic">ω</mml:mi></mml:msup><mml:mo>=</mml:mo><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow><mml:mi mathvariant="italic">β</mml:mi><mml:mi>c</mml:mi></mml:mrow><mml:mi mathvariant="italic">ω</mml:mi></mml:msubsup><mml:mo>/</mml:mo><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mi mathvariant="italic">β</mml:mi></mml:msub><mml:mspace linebreak="nobreak" width="0.25em"/><mml:mspace width="0.25em" linebreak="nobreak"/><mml:mtext>and so</mml:mtext><mml:mspace linebreak="nobreak" width="0.25em"/><mml:mspace width="0.25em" linebreak="nobreak"/><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow><mml:mi mathvariant="italic">β</mml:mi><mml:mi>c</mml:mi></mml:mrow><mml:mi mathvariant="italic">ω</mml:mi></mml:msubsup><mml:mo>=</mml:mo><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mi mathvariant="italic">β</mml:mi></mml:msub><mml:msup><mml:mtext>CMF</mml:mtext><mml:mi mathvariant="italic">ω</mml:mi></mml:msup></mml:mrow></mml:math></disp-formula>

          A heuristic expression (showing explicitly that 0 <inline-formula><mml:math id="M418" display="inline"><mml:mo>≤</mml:mo></mml:math></inline-formula> CMF<inline-formula><mml:math id="M419" display="inline"><mml:mrow><mml:msup><mml:mi/><mml:mi mathvariant="italic">ω</mml:mi></mml:msup><mml:mo>≤</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula>) is; CMF<inline-formula><mml:math id="M420" display="inline"><mml:mrow><mml:msup><mml:mi/><mml:mi mathvariant="italic">ω</mml:mi></mml:msup><mml:mo>=</mml:mo><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow><mml:mi mathvariant="italic">β</mml:mi><mml:mi>c</mml:mi></mml:mrow><mml:mi mathvariant="italic">ω</mml:mi></mml:msubsup><mml:mo>/</mml:mo><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mi mathvariant="italic">β</mml:mi><mml:mi mathvariant="italic">ω</mml:mi></mml:msubsup><mml:mo>=</mml:mo><mml:msup><mml:mfenced open="[" close="]"><mml:mrow><mml:msub><mml:mo>∑</mml:mo><mml:mi>i</mml:mi></mml:msub><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msub><mml:mi mathvariant="italic">ω</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>J</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi mathvariant="italic">β</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>J</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfenced><mml:mrow><mml:msub><mml:mi mathvariant="normal">VDR</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>J</mml:mi></mml:mrow></mml:msub><mml:mo>≥</mml:mo><mml:msub><mml:mi mathvariant="italic">δ</mml:mi><mml:mi mathvariant="normal">thr</mml:mi></mml:msub></mml:mrow></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>z</mml:mi><mml:mo>/</mml:mo><mml:msub><mml:mo>∑</mml:mo><mml:mi>i</mml:mi></mml:msub><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msub><mml:mi mathvariant="italic">ω</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>J</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi mathvariant="italic">β</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>J</mml:mi></mml:mrow></mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>z</mml:mi><mml:mo>=</mml:mo><mml:msup><mml:mfenced close="]" open="["><mml:mrow><mml:msub><mml:mo>∑</mml:mo><mml:mi>i</mml:mi></mml:msub><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msub><mml:mi mathvariant="italic">ω</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>J</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi mathvariant="italic">β</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>J</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfenced><mml:mrow><mml:msub><mml:mi mathvariant="normal">VDR</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>J</mml:mi></mml:mrow></mml:msub><mml:mo>≥</mml:mo><mml:msub><mml:mi mathvariant="italic">δ</mml:mi><mml:mi mathvariant="normal">thr</mml:mi></mml:msub></mml:mrow></mml:msup><mml:mo>/</mml:mo><mml:msub><mml:mo>∑</mml:mo><mml:mi>i</mml:mi></mml:msub><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msub><mml:mi mathvariant="italic">ω</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>J</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi mathvariant="italic">β</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>J</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>. The explicit link with the unweighted stats is to employ <inline-formula><mml:math id="M421" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mi mathvariant="italic">β</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> when calculating <inline-formula><mml:math id="M422" display="inline"><mml:mrow><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow><mml:mi mathvariant="italic">β</mml:mi><mml:mi>c</mml:mi></mml:mrow><mml:mi mathvariant="italic">ω</mml:mi></mml:msubsup></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M423" display="inline"><mml:mrow><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow><mml:mi mathvariant="italic">β</mml:mi><mml:mi>f</mml:mi></mml:mrow><mml:mi mathvariant="italic">ω</mml:mi></mml:msubsup></mml:mrow></mml:math></inline-formula> from CMF<sup><italic>ω</italic></sup>.

            <disp-formula id="App1.Ch1.S1.E16.19" content-type="subnumberedoff"><label>A7c</label><mml:math id="M425" display="block"><mml:mrow><mml:msup><mml:mtext>FMF</mml:mtext><mml:mi mathvariant="italic">ω</mml:mi></mml:msup><mml:mo>=</mml:mo><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow><mml:mi mathvariant="italic">β</mml:mi><mml:mi>f</mml:mi></mml:mrow><mml:mi mathvariant="italic">ω</mml:mi></mml:msubsup><mml:mo>/</mml:mo><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mi mathvariant="italic">β</mml:mi></mml:msub><mml:mspace linebreak="nobreak" width="0.25em"/><mml:mspace linebreak="nobreak" width="0.25em"/><mml:mtext>and so</mml:mtext><mml:mspace width="0.25em" linebreak="nobreak"/><mml:mspace linebreak="nobreak" width="0.25em"/><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow><mml:mi mathvariant="italic">β</mml:mi><mml:mi>f</mml:mi></mml:mrow><mml:mi mathvariant="italic">ω</mml:mi></mml:msubsup><mml:mo>=</mml:mo><mml:msup><mml:mtext>FMF</mml:mtext><mml:mi mathvariant="italic">ω</mml:mi></mml:msup><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mi mathvariant="italic">β</mml:mi></mml:msub></mml:mrow></mml:math></disp-formula></p>
      <p id="d2e7623">The <inline-formula><mml:math id="M426" display="inline"><mml:mrow><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mi mathvariant="italic">β</mml:mi><mml:mi mathvariant="italic">ω</mml:mi></mml:msubsup><mml:mo>=</mml:mo><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mi mathvariant="italic">β</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> forcing guarantees that the lidar-profile-integrated differences of <inline-formula><mml:math id="M427" display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow><mml:mi mathvariant="italic">β</mml:mi><mml:mi>f</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mo>〈</mml:mo><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow><mml:mi mathvariant="italic">β</mml:mi><mml:mi>f</mml:mi></mml:mrow></mml:msub><mml:mo>-</mml:mo><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow><mml:mi mathvariant="italic">β</mml:mi><mml:mi>f</mml:mi></mml:mrow><mml:mi mathvariant="italic">ω</mml:mi></mml:msubsup><mml:mo>〉</mml:mo></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M428" display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow><mml:mi mathvariant="italic">β</mml:mi><mml:mi>c</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mo>〈</mml:mo><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow><mml:mi mathvariant="italic">β</mml:mi><mml:mi>c</mml:mi></mml:mrow></mml:msub><mml:mo>-</mml:mo><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow><mml:mi mathvariant="italic">β</mml:mi><mml:mi>c</mml:mi></mml:mrow><mml:mi mathvariant="italic">ω</mml:mi></mml:msubsup><mml:mo>〉</mml:mo></mml:mrow></mml:math></inline-formula> <italic>of each profile</italic> cancel each other out <inline-formula><mml:math id="M429" display="inline"><mml:mrow><mml:mo>(</mml:mo><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow><mml:mi mathvariant="italic">β</mml:mi><mml:mi>f</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow><mml:mi mathvariant="italic">β</mml:mi><mml:mi>c</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>.</p>
      <p id="d2e7769">The results shown in Fig. A5 indicate that the “<inline-formula><mml:math id="M430" display="inline"><mml:mi mathvariant="italic">ω</mml:mi></mml:math></inline-formula>” weighting can effectively incite what we attribute to artificial <inline-formula><mml:math id="M431" display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow><mml:mi mathvariant="italic">β</mml:mi><mml:mi>c</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M432" display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow><mml:mi mathvariant="italic">β</mml:mi><mml:mi>f</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> spikes<fn id="App1.Ch1.Footn24"><p id="d2e7811">The <inline-formula><mml:math id="M433" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ω</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>J</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi mathvariant="italic">β</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>J</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> weighting appears to enhance what would otherwise be nondescript points in the <inline-formula><mml:math id="M434" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">β</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>J</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> profile values.</p></fn> (the lidar profiles show no corresponding anomalies), These spikes aside, the CM vs FM classification using a weighting approach generally showed no significant <inline-formula><mml:math id="M435" display="inline"><mml:mrow><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow><mml:mi mathvariant="italic">β</mml:mi><mml:mi>c</mml:mi></mml:mrow><mml:mi mathvariant="italic">ω</mml:mi></mml:msubsup></mml:mrow></mml:math></inline-formula> vs. <inline-formula><mml:math id="M436" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow><mml:mi mathvariant="italic">β</mml:mi><mml:mi>c</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> changes. Accordingly, any attempt to improve the quality of <inline-formula><mml:math id="M437" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow><mml:mi mathvariant="italic">β</mml:mi><mml:mi>c</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> by VDR-noise-based weighting results in either very little change or is the victim of significant outliers generated by the VDR weighting. Unlike the VDR weighting approach improvements (indicated by Fig. A2) there appears to be no significant advantage in a VDR-based filtering of the CM/FM classification.</p><fig id="FA5"><label>Figure A5</label><caption><p id="d2e7905"><inline-formula><mml:math id="M438" display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow><mml:mi mathvariant="italic">β</mml:mi><mml:mi>c</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M439" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M440" display="inline"><mml:mrow><mml:mo>〈</mml:mo><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow><mml:mi mathvariant="italic">β</mml:mi><mml:mi>c</mml:mi></mml:mrow></mml:msub><mml:mo>-</mml:mo><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow><mml:mi mathvariant="italic">β</mml:mi><mml:mi>c</mml:mi></mml:mrow><mml:mi mathvariant="italic">ω</mml:mi></mml:msubsup><mml:mo>〉</mml:mo></mml:mrow></mml:math></inline-formula> vs. time (top) and  <inline-formula><mml:math id="M441" display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow><mml:mi mathvariant="italic">β</mml:mi><mml:mi>f</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M442" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M443" display="inline"><mml:mrow><mml:mo>〈</mml:mo><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow><mml:mi mathvariant="italic">β</mml:mi><mml:mi>f</mml:mi></mml:mrow></mml:msub><mml:mo>-</mml:mo><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow><mml:mi mathvariant="italic">β</mml:mi><mml:mi>f</mml:mi></mml:mrow><mml:mi mathvariant="italic">ω</mml:mi></mml:msubsup><mml:mo>〉</mml:mo></mml:mrow></mml:math></inline-formula> vs. time (bottom). Example of the 23 July 2007 event.</p></caption>
          
          <graphic xlink:href="https://amt.copernicus.org/articles/19/4553/2026/amt-19-4553-2026-f14.png"/>

        </fig>


</sec>
</app>

<app id="App1.Ch1.S2">
  <label>Appendix B</label><title>Acronym and symbol glossary</title>
      <p id="d2e8032"><table-wrap position="anchor"><oasis:table><oasis:tgroup cols="2">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="justify" colwidth="6.8cm"/>
     <oasis:tbody>
       <oasis:row>
         <oasis:entry colname="col1">AERONET</oasis:entry>
         <oasis:entry colname="col2">AErosol RObotic NETwork</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">AEROCAN</oasis:entry>
         <oasis:entry colname="col2">Canadian sub-network of AERONET</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">AHSRL</oasis:entry>
         <oasis:entry colname="col2">Arctic High Spectral Resolution Lidar</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">AOD</oasis:entry>
         <oasis:entry colname="col2">Aerosol Optical Depth</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">APS</oasis:entry>
         <oasis:entry colname="col2">Aerodynamic Particle Sizer</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">a.s.l.</oasis:entry>
         <oasis:entry colname="col2">Above Sea Level</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">CAA</oasis:entry>
         <oasis:entry colname="col2">Canadian Arctic Archipelago</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">CARRA</oasis:entry>
         <oasis:entry colname="col2">Copernicus Arctic Regional ReAnalysis</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">CALIOP</oasis:entry>
         <oasis:entry colname="col2">Cloud-Aerosol Lidar with Orthogonal    Polarization</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">CANDAC</oasis:entry>
         <oasis:entry colname="col2">Canadian Network for the Detection of   Atmospheric Change</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">CM</oasis:entry>
         <oasis:entry colname="col2">Coarse Mode</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">CMF</oasis:entry>
         <oasis:entry colname="col2">Coarse Mode Fraction (1-FMF)</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">CW</oasis:entry>
         <oasis:entry colname="col2">ClockWise</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">CCW</oasis:entry>
         <oasis:entry colname="col2">CounterClockWise</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">DB</oasis:entry>
         <oasis:entry colname="col2">Deep Blue (MODIS AOD retrieval  algorithmover bright surfaces)</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">DT</oasis:entry>
         <oasis:entry colname="col2">Dark Target (MODIS AOD retrieval   algorithm over dark targets (water and   vegetated land)</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">DOD</oasis:entry>
         <oasis:entry colname="col2">Dust Optical Depth</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">DR</oasis:entry>
         <oasis:entry colname="col2">Depolarisation Ratio</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">ECCC</oasis:entry>
         <oasis:entry colname="col2">Environment and Climate Change Canada</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">FM</oasis:entry>
         <oasis:entry colname="col2">Fine Mode</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">FMF</oasis:entry>
         <oasis:entry colname="col2">Fine Mode Fraction (MODIS product)</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">HLD</oasis:entry>
         <oasis:entry colname="col2">High Latitude Dust</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">INP</oasis:entry>
         <oasis:entry colname="col2">Ice Nucleating Particle</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">IR</oasis:entry>
         <oasis:entry colname="col2">InfraRed</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">KLRS</oasis:entry>
         <oasis:entry colname="col2">Kluane Lake Research Station</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">MISR</oasis:entry>
         <oasis:entry colname="col2">Multi-angle Imaging SpectroRadiometer</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">MINX</oasis:entry>
         <oasis:entry colname="col2">MISR INteractive eXplorer</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">MODIS</oasis:entry>
         <oasis:entry colname="col2">Moderate Resolution Imaging   Spectroradiometer</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">NA</oasis:entry>
         <oasis:entry colname="col2">Not Available</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">NASA</oasis:entry>
         <oasis:entry colname="col2">National Aeronautics and Space   Administration</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">OD</oasis:entry>
         <oasis:entry colname="col2">Optical Depth</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">0PAL</oasis:entry>
         <oasis:entry colname="col2">Zero Altitude PEARL Auxiliary Laboratory</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">OPS</oasis:entry>
         <oasis:entry colname="col2">Optical Particle Sizer</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">PEARL</oasis:entry>
         <oasis:entry colname="col2">Polar Environment Atmospheric Research   Laboratory</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">PDR</oasis:entry>
         <oasis:entry colname="col2">Particle Depolarization Ratio</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">PMSD</oasis:entry>
         <oasis:entry colname="col2">Particle-Mass Size Distribution</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">PVSD</oasis:entry>
         <oasis:entry colname="col2">Particle-Volume Size Distribution</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">R</oasis:entry>
         <oasis:entry colname="col2">Correlation Coefficient</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">RE</oasis:entry>
         <oasis:entry colname="col2">Residual Error</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">RMS</oasis:entry>
         <oasis:entry colname="col2">Root Mean Square</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">RS</oasis:entry>
         <oasis:entry colname="col2">Remote Sensing</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">sr</oasis:entry>
         <oasis:entry colname="col2">Steradian</oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table></table-wrap></p>
      <p id="d2e8448"><table-wrap position="anchor"><oasis:table><oasis:tgroup cols="2">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="justify" colwidth="7cm"/>
     <oasis:tbody>
       <oasis:row>
         <oasis:entry colname="col1">SD</oasis:entry>
         <oasis:entry colname="col2">Standard Deviation</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">SWIR</oasis:entry>
         <oasis:entry colname="col2">Short-Wave InfraRed</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">UTC</oasis:entry>
         <oasis:entry colname="col2">Coordinated Universal Time</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">UV</oasis:entry>
         <oasis:entry colname="col2">UltraViolet</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">VDR</oasis:entry>
         <oasis:entry colname="col2">Volume Depolarization Ratio</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">WMO</oasis:entry>
         <oasis:entry colname="col2">World Meteorological Organization</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M444" display="inline"><mml:mi mathvariant="italic">β</mml:mi></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">Backscatter Coefficient</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M445" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">β</mml:mi><mml:mi>c</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">CM Backscatter Coefficient</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M446" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mi mathvariant="italic">β</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">Particulate Backscatter Optical Depth</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M447" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow><mml:mi mathvariant="italic">β</mml:mi><mml:mo>,</mml:mo><mml:mi>c</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">CM <inline-formula><mml:math id="M448" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mi mathvariant="italic">β</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M449" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow><mml:mi mathvariant="italic">β</mml:mi><mml:mo>,</mml:mo><mml:mi>f</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">FM <inline-formula><mml:math id="M450" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mi mathvariant="italic">β</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M451" display="inline"><mml:mrow><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mi>c</mml:mi><mml:mi>l</mml:mi></mml:msubsup></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">Lidar CM AOD</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M452" display="inline"><mml:mrow><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mi>f</mml:mi><mml:mi>l</mml:mi></mml:msubsup></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">Lidar FM AOD</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M453" display="inline"><mml:mrow><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mi>c</mml:mi><mml:mi mathvariant="normal">O</mml:mi></mml:msubsup></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">0PAL CM AOD</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M454" display="inline"><mml:mrow><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow><mml:mi>c</mml:mi><mml:mo>,</mml:mo><mml:mn mathvariant="normal">1.5</mml:mn></mml:mrow><mml:mi mathvariant="normal">O</mml:mi></mml:msubsup></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">0PAL cloud-screened (L 1.5) CM AOD</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M455" display="inline"><mml:mrow><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mi>c</mml:mi><mml:mi mathvariant="normal">P</mml:mi></mml:msubsup></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">PEARL CM AOD</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M456" display="inline"><mml:mrow><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow><mml:mi>c</mml:mi><mml:mo>,</mml:mo><mml:mn mathvariant="normal">1.5</mml:mn></mml:mrow><mml:mi mathvariant="normal">P</mml:mi></mml:msubsup></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">PEARL cloud-screened (L 1.5) CM AOD</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M457" display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi>c</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">CM Lidar Ratio</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M458" display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi>f</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">FM Lidar Ratio</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M459" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi>c</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">Particle-Volume Concentration</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M460" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">δ</mml:mi><mml:mi>c</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">CM PDR</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M461" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">δ</mml:mi><mml:mi>f</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">FM PDR</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M462" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">δ</mml:mi><mml:mi mathvariant="normal">thr</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">VDR threshold</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M463" display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mi>c</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">0PAL minus PEARL CM AOD difference   (<inline-formula><mml:math id="M464" display="inline"><mml:mrow><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mi>c</mml:mi><mml:mi mathvariant="normal">O</mml:mi></mml:msubsup><mml:mo>-</mml:mo><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mi>c</mml:mi><mml:mi mathvariant="normal">P</mml:mi></mml:msubsup></mml:mrow></mml:math></inline-formula>)</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">ws</oasis:entry>
         <oasis:entry colname="col2">Wind Speed (km h<sup>−1</sup>)</oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table></table-wrap></p>
</app>
  </app-group><notes notes-type="codeavailability"><title>Code availability</title>

      <p id="d2e8942">MATLAB codes employed for computations reported in this manuscript can be obtained from Seyed Ali Sayedain (seyed.ali.sayedain@usherbrooke.ca).</p>
  </notes><notes notes-type="dataavailability"><title>Data availability</title>

      <p id="d2e8948">AERONET data are available for download at <ext-link xlink:href="https://doi.org/10.17616/R3VK9T" ext-link-type="DOI">10.17616/R3VK9T</ext-link> (Lind and Gupta, 2023). The PEARL AHSRL data are accessible from the University of Wisconsin HSRL data archives at <uri>https://hsrl.ssec.wisc.edu/by_site/2/bscat/2007/07/</uri> (last access: 2 December 2025). APS data can be obtained from Seyed Ali Sayedain (seyed.ali.sayedain@usherbrooke.ca). ECCC hourly climate data for different stations can be downloaded at <uri>https://climate-change.canada.ca/climate-data/#/hourly-climate-data</uri> (last access: 2 December 2025). MODIS Terra and Aqua images and products along with MISR datasets can be downloaded from the Earth Science Data Systems (ESDS) at <uri>https://search.earthdata.nasa.gov/search</uri> (last access: 2 December 2025). Sentinel-2 data can be downloaded from Copernicus Browser (<uri>https://browser.dataspace.copernicus.eu/</uri>, last access: 2 December 2025). CARRA data at different levels (single, pressure, height and model) can be downloaded from the Copernicus Climate Data Store (CDS) at <uri>https://cds.climate.copernicus.eu/datasets</uri> (last access: 2 December 2025). Underlying supplementary data related to this article can be accessed at <ext-link xlink:href="https://doi.org/10.5281/zenodo.20561203" ext-link-type="DOI">10.5281/zenodo.20561203</ext-link> (Sayedain and O'Neill, 2026).</p>
  </notes><notes notes-type="authorcontribution"><title>Author contributions</title>

      <p id="d2e8976">SAS: writing – original draft preparation – review and editing, visualization, investigation, conceptualization, methodology, formal analysis, data curation, validation, software, resources. NTO: writing – review and editing, supervision, visualization, conceptualization, methodology, formal analysis, data curation, validation, funding acquisition, resources. KR: review and editing, data curation, resources. PGB: review and editing, data curation, validation. RC: review and editing, data curation, validation, funding acquisition, resources. PLH: review and editing, data curation, validation, funding acquisition, resources. JK: review and editing, data curation, validation, funding acquisition.</p>
  </notes><notes notes-type="competinginterests"><title>Competing interests</title>

      <p id="d2e8982">The contact author has declared that none of the authors has any competing interests.</p>
  </notes><notes notes-type="disclaimer"><title>Disclaimer</title>

      <p id="d2e8988">Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this paper. The authors bear the ultimate responsibility for providing appropriate place names. Views expressed in the text are those of the authors and do not necessarily reflect the views of the publisher.</p>
  </notes><ack><title>Acknowledgements</title><p id="d2e8994">Valuable in-kind support was provided by the AEROCAN network of Environment and Climate Change Canada (ECCC), the NASA AERONET network, the Canada Research Chairs Program (CRC), and the Canadian Network for the Detection of Atmospheric Change (PAHA/CANDAC) team. We also acknowledge the use of imagery from the NASA Worldview application (<uri>https://worldview.earthdata.nasa.gov</uri>, last access: 2 December 2025), part of the NASA Earth Science Data and Information System (ESDIS). We also acknowledge the use of Sentinel-2 data from the Copernicus Programme and MISR data provided by NASA. We thank ESA and NASA for making these remote-sensing datasets freely accessible.</p></ack><notes notes-type="financialsupport"><title>Financial support</title>

      <p id="d2e9003">Financial support was provided by the Discovery Grant (DG) program of the Natural Sciences and Engineering Research Council of Canada (grant nos. RGPIN-2023-04943, RGPIN-2022-03785, RGPIN-2022-04963), the Canada Research Chairs Program (CRC-2020-00285) and the SACIA-2 (Signatures of Aerosol-Cloud Interaction over the Arctic) project funded by the Canadian Space Agency's ESS-DA (Earth System Science – Data Analysis) program (grant no. 21SUASACOA). SACIA-2 is a collaborative project with Dalhousie University and the Université de Montréal.</p>
  </notes><notes notes-type="reviewstatement"><title>Review statement</title>

      <p id="d2e9009">This paper was edited by Sebastian Schmidt and reviewed by two anonymous referees.</p>
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